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 of two cards each, all of them 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 one hand contains two aces, one contains two jacks, and one contains an ace and a jack (a blackjack). You turn over one of the cards and see that it's an ace. What is the probability that that hand is the blackjack?


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