"A conversation"

Hey there folks!

I am trying to explain this to someone else, an ESL guy. The sentence we're looking at is this:

"Remember we had a conversation about this last week? Well, turned out you were right." 
I know that the indefinite article before "conversation" is natural (it is too my ears), but I can't explain it to the other person, who can't figure out why "a" is better than "the".

The best that I can do is say, well, there are many conversations and although you CAN use "the", a conversation ain't really all that specific even if both people know about it and can remember it. On the other hand,
"Remember we had THE committee over that day?"

A committee is darn unique, there aren't that many, so I might be inclined to use "the" in that case.

That's the best I could do. Could I of done better to explain this?