AA vs. AA 2 out of 3 hands?

[Mr. Curious]

I was playing at a B&M last night when I saw this happen. The first hand I had pocket aces and the guy to my right did as well. Two hands later two other people had them. So I thought I would take a stab at trying to figure out the probability of it happening.

For there to be AA vs AA, the odds are 3/51 * 2/50 * 1/49 = .00004801%

For this to have happened again, it is just .0004801^2, right?
I don't need to figure out the odds of it not happening in the second hand, do I?