You're welcome, Jisu.
I just read the post again. Never thought much about it, but now I realize it can be very tricky, or confusing. If I may, I'd like to stress one point:
When there are only two people or things in a group, and you're talking about adding another one, you're looking for any one which will make it three. It's not a specific one. It's indefinite, hence we use the indefinite article "a." I just drank two glasses of beer. I think I'll have a third one.
But once that glass becomes part of the group, making three, It's no longer indefinite. That was the third glass of beer I drank tonight. We're now talking about a specific glass - a definite one.
That doesn't mean if there are three friends, Joe is #1, Bill is #2, and Ed is #3. A minute ago I saw three of you. Now there are only two. What happened to the third guy? We're talking about a definite guy. But if the speaker isn't sure, and he thinks maybe there are only two, he'd say, "Hey, didn't I see a third guy a minute ago?"
And now that we know Brahms wrote four symphonies, the third symphony will always be the third one he wrote.