Obviously, it's all at the discretion of the house, but
usually it works like this:
You pay X amount. Now you're out X dollars. If you happen to win, you get Y amount. You've won Y - X dollars. You don't have to pay an entry fee for most gambling, because most of the time the house wins. Also, they aren't paying X times 3 (in these examples), because you've already put in X. I'm not real strong on math, but I guess that means they're paying X times 2. It's a loss, yes, but not as big of one.
Your assumptions (a and b) are correct (if the ratios are right), but the bettor is not really MAKING 3 dollars; s/he's making 2. Which is pretty much what you said.
As for the odds, now that it's being discussed, I'm not so sure how it goes. The way I remember it is that in "live action" betting (i.e., horse racing, etc., the kind we're interested in) bets were taken until the race/fight actually began, at which point the odds are locked in. Everyone who got a bet in before the official start of the match has the same odds, it just depends how much you bet. That way, if the favorite wins, the house doesn't get screwed over too badly. But like I said, I'm not really sure about that any more . . . And, obviously, every "house" is different and the way things are run is always different, even within the same day at the same location.