A Poker Puzzle

I receive this problem today, from Stan Wagon’s Problem of the Week. I slightly reword it:

You are playing stud poker (5 cards dealt, no exchanging of cards) with a few friends and a standard 52-card deck. It’s your lucky day and by some miracle you are guaranteed to end up with a full house, but only if you correctly choose the best full house. Which full house should you choose? (i.e., which full house has the highest probability of winning?)

I gave this problem some thought. It is not as easy as it looks. What is the answer?

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