1. I found this explanation of WOULD from Collin's English Usage:

"possible situations
You use should or would to say that something is certain to happen in particular circumstances.

After `I' or `we' you can use either should or would.
I should be very unhappy on the continent.
We would be glad to have money of our own.
If I were Tim, I'd be a bit uneasy.

After any other pronoun or noun, you use would. You do not use should.
Few people would agree with this as a general principle.
He would be disappointed, but he would understand."

I don't quite understand what the above means by 'particular circumstances'? Why 'WILL' is not used in the above sentences? Why WOULD is used? Is it because those 'circumstances' are not realised yet and are just hypotheical?

2. FURTHERMORE, I found everyday use of 'would' seems to be related to 'probabilty' / 'prediction'. Some examples are:

From http://grammar.ccc.commnet.edu/GRAMMAR/auxiliary.htm :

"Finally, would can express a sense of probability:
  • I hear a whistle. That would be the five o'clock train."
In the same website, the writer wrote:
"In England, shall is used to express the simple future for first person I and we, as in "Shall we meet by the river?" Will would be used in the simple future for all other persons. Using will in the first person would express determination on the part of the speaker, as in "We will finish this project by tonight, by golly!" Using shall in second and third persons would indicate some kind of promise about the subject, as in "This shall be revealed to you in good time.""

Do all the 'would's used here mean probability or prediction with confidence? I think I have encountered similar use in my past reading, but it seems it is rarely mentioned or explained in dictionaries!

Can anyone help?

1) The example of would / should (old fashioned) is subjunctive mood, usually after a conditional, or an implied conditional, which states something contrary to fact.

I should be very happy (if I were) on the continent. (I am not on the continent)
We would be glad If we had money of our own. (We do not have any money

Will is not used, because it is something that happens in the future, and there is nothing contrary to fact:

I will go home early if I finish my work. (I am working now)
When I save enough money, I will buy the tickets.
If I had saved enough money (but I didn't), I would have bought the tickets.

2) Yes, "would" can have the meaning of "I'm pretty sure, but not absolutely sure."
The doorbell is ringing, and it is the time of day when the postman usually comes.
"That would be the postman at the door." We also say "That must be the postman."
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Hi AlpheccaStars, I checked the Oxford and Longman dictionaries once again. Your first explanation is understandable (that is no.2 in the list below). Yet the 2nd one 'I'm pretty sure' is still missing:

1. used as the past form of will when reporting what sb has said or thought:
2. used for talking about the result of an event that you imagine:
3. used for describing a possible action or event that did not in fact happen, because sth else did not happen first
4. so that / in order that sb/sth ~ used for saying why sb does sth:
5. wish (that) sb/sth ~ used for saying what you want to happen:
6. used to show that sb/sth was not willing or refused to do sth
7. used to ask sb politely to do sth
8. used in polite offers or invitations:
9. would like, love, hate, prefer, etc. sth / (sb) to do sth
10. would imagine, say, think, etc. (that) … used to give opinions that you are not certain about
11. I would … used to give advice:
12. used for talking about things that often happened in the past
13. (usually disapproving) used for talking about behaviour that you think is typical:
14. would that … (literary) used to express a strong wish

"That would be the postman at the door." - what is the meaning of would here in the list above? I have to say I think I often think 'would' means 'highly likely' in many writings, but I find it's strange that it is rarely - if not never - listed in dictionaries. Or have I misunderstood something?

Thank you ...
Can anyone help me? I have been puzzled by this question for years ... Emotion: sad
Chacha: Now that I think about the examples
That would be the 5 o'clock train...
That would be the postman...
These are examples of definitions 5, 10 or 14.
That would be the postman. - I might be expressing a wish and hope it is the postman (I am expecting a package)
That would be the 5 o'clock train... - it could be #10, he's giving an opinion that he is not certain about, or #5, because he is expecting someone on the train, or he is getting ready to get on the train.
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Thanks, AlpheccaStars!

I am grateful to you - but I have the feeling that we're trying to twist the meaning of 'that would be the postman' into 'official' explanations of dictionaries ....Emotion: surprise

After more search, I find this definition in Collin's Dictionary (the first use in my first post is from Collin's Grammer):

4 would
You use would, or would have with a past participle, to indicate that you are assuming or guessing that something is true, because you have good reasons for thinking it.
You wouldn't know him.
His fans would already be familiar with Caroline.
That would have been Della's car.
He made a promise to his great-grandfather? That would have been a long time ago.
It was half seven; her mother would be annoyed because he was so late.

I wonder if this entry better explains your 'I'm pretty sure' explanation ... The only thing I am worried in the above entry is that it doesn't specify if I can use 'would' this way with the simple present tense to describe some general opinions / general statements. But I also searched for sentences in various texts which seem to be using 'would' this way (please tell me what you think):

- The best practice of these endeavors would be UNESCO’s World Culture Report of 2000. (it is the author's opinion, and he is indicating that s/he has good reasons for this).
- The creative industries are not a self-sufficient production system. The sector interacts with other economic and cultural sectors, which invariably would result in an extended mapping of both tangible and intangible values brought to society and the economy at
large.(the author is making a more or less general statement here, but s/he uses would rather than will to avoid absolute certainty. But 'would' still indicate that s/he has good reasons for this statement).
- The first alternative would lead to an honourable and heroic death in the service of a minority already culturally well-supplied and the
demise of PSM would be applauded by commercial media.

I think this use of would emphasises the author's beliefs that something is true, but in effect, it indicates a sense of high probability like the use of 'is very likely to'. What do you think?

I feel weird since this use is not documented in Longman and Oxford dictionaries.Emotion: thinking