TPTK vs PP of same

That title may be a bit confusing.

Anyway, here is the scenario I ran into last night in a tourney that knocked me out. Not looking to gripe about the hand, but to learn about the probabilities and identify this.

I had AQ and made a 3xbb bet preflop. I think there were 3 callers. Flop comes xQx. Guy before me makes a small bet, I go pot sized raise, he re-raises. I call. A on turn. I make a 2/3 size bet, he goes all in. I call. He shows QQ to beat my two pair and I am done.

The question is not really how to play it as much as this:

When you have paired any card on the board with a card in your hand, what are the odds that someone else is holding that same card as a pocket pair in their hand?

The probability of one particular person having exactly the pocket pair when you have already seen 2 of the cards after the flop is (2/47)(1/46) which is about .00093 or about 1/10 of one percent. In the case of QQ, you can be assured that anyone holding QQ before the flop is in the flop now, so really you want the odds of anyone holding QQ before the flop. This is approximately 9 times greater with a full table, so realistically there is close to a 1% chance of it happening. It is no fun for this to happen, and it is extremely unlikely, and usually a bad idea to assume your opponent has this hand because of the thin odds. In the particular hand you cited, it is far more likely they hold a different set, but you are just as dead. One of the few times you can spot this happening to you is if you have AK and the other guy has AA or KK and makes a sizable raise pre-flop. The flop comes with an A and a K and you make a big bet and he goes all in. If you have a strong read on this player that he only raises big preflop with KK or AA, you can safely fold (of course if you had this read on him you should have folded preflop!). A strong read is better than pure odds.

Yeah the point here isn't what are the odds he made that set, but what are the odds that you would get that kind of action on the flop unless someone can beat TPTK? Those odds are not good, especially if there were no draws out. Even then it's rare to see someone re re raise with a draw on the flop. Also small bet into pre flop raiser and then a re raise almost always sez monster.

He only called a 3XBB raise with QQ? I want to know what the odds are that Mr. QQ will still have money to play with in a week.