Probably blackjack

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This is a classic probability puzzle. I just made up the story.


You are playing Blackjack and are lucky enough to have a psychic parrot on your shoulder. You are dealt three hands, both cards in each hand face down. Because you have the help of the psychic parrot, you are only allowed to turn over one of the six cards. The parrot tells you that on of the hands contains two aces, one contains two jacks, and the other contains a blackjack (and ace and an jack). You turn over one of the cards and see it is an ace. What is the probability that that hand is in fact a blackjack?


I got the idea for this one from The Riddle of Scheherazade: And Other Amazing Puzzles by Raymond Smullyan.