A question of probability

Thanks a lot guys for the input. I realize the question that I asked could be understood in different ways. I was actually asking what were the odds of the event happening and not just the odds as seen by the players.
For those that were wondering there was no option for a flush.

What's the difference between the event odds and the odds as seen by the players?

By event odds I meant 'what were the chances of the next two cards being aces after the flop?' However, that takes into consideration the fact that we know two of the aces are already out there. (A very non-poker way of looking at things.)
The odds as seen from the players point of view the players, and in particular the villain who can only see the one ace in front of him.

Originally Posted by Tasha

By event odds I meant 'what were the chances of the next two cards being aces after the flop?' However, that takes into consideration the fact that we know two of the aces are already out there.

I'm not sure how this is any different from what was already explained. We provided the odds of: knowing that one ace was already 'out', and that there were 45 unknown cards on the flop (two in hero's hand, two in villain's, and three on the board after the flop, out of a deck of 52), how often will both the turn and the river come an ace. In this case, the odds are as stated above, 0.3030 or ~330 to 1.

Originally Posted by Tasha

The odds as seen from the players point of view the players, and in particular the villain who can only see the one ace in front of him.

The odds of winning against QQ as seen from the player holding AQ on a board of x-x-Q are as detailed above.

As for the player holding QQ on such a board, if they are really concerned about the turn and river coming aces, they would also have to include an Ace in villain's hand; as such the calculations are pretty much the same -- depending on whether we treat the villain's second hole card as unknown or not.

If, for whatever reason, the player holding QQ would like to arbitrarily calculate the probability of the turn and river coming aces when he or she has no information on villain's hole cards, the odds are (4/47) * (4/46).

If you want to know the simple probability of a turn and river both coming aces, when we have no information on anyone's hole cards, the odds are (4/49) * (3/48).