The first answer is close, but incorrect. That would be the answer if you asked, "what is the probability of pocket aces, pocket kings, and pocket queens being drawn as the first hand in three different games (considering the deck is reshuffled after every game and no cards are discarded before the draw)"
I did a fairly quick solution, and it most likely is not what you are looking for. I don't know the order in which the pocket cards were drawn so my model has the first three hands being pocket cards. I assume no cards are discarded at any point and that the deck is fair(meaning there is no foul play and it is random). This solution would have the lowest probability of happening. If you have the order, I can adjust my solution(assuming I am doing it correct)
I have the problem worked out on my tablet and I can insert a screenshot of the work. It's a fairly simple conditional probability problem.
P(pocket A's, pocket k's, and pocket q's)=3/25448150