James rules for your table:

There are 9 people. Everyone always plays to flop if they get an ace (loosely). You are facing one person after the flop. You have an Ace, the flop has an ace, what is the probability that person across from you has an ace?

Thats the question I answered. It is not at all the same as dealing someone two cards from a 47 card deck.

edit: My answer is actually slightly off, but only a bit, because it is the probability that one or two villans get dealt one or two of the remaining aces preflop conditioned on your hand and the flop, and since in this outcome only one villan could possibly have gotten an ace that is overcounting by a bit.

As a test if you have a deck of cards you can put an ace and a duece in your hand, put an ace king queen in a flop. And then deal out 8 other

hands over and over and count how many times one or more of those 8 hands has an ace (alternatively you can just thumb through the top 16 cards of a 47 card deck shuffled over and over). I am saying its bout half. Now you figure if your at a table where everyone is playing their aces to flop, those other aces always end up at the flop.