Like many other situations in learning a language, explanation
won't help -- not much anyway. You just have to experience these
words in their many, many contexts for quite a long time before you
understand exactly how to use them. No explanation exists
which easily covers all the possible uses of these words. You
almost have to ask about one sentence at a time.
That said, in the sentences you wrote, in the first pair, it doesn't make a lot of difference which you use -- the "will of probability" or the "would of probability". Both mean, in a broad sense, that John is probably busy now. Perhaps the second, with would,
indicates a little less certainty. This is my
interpretation. There may be others. Personally, I don't
use either of these very much.
In the second pair, if we contrast the use of will and would, the use of will makes the situation more definite. It sounds like the chosen solution really will be implemented. With would,
it seems that the solution might be implemented only if the right
situation were to come about, and it's not certain that such a
situation will come up. The idea is that if the people concerned
ever need the solution -- and no one knows if they will need it -- they
know which solution is best.
CJ