Puzzle #247: Full House

From an ordinary 52-card deck of playing cards, you have just been dealt the ace of diamonds and the king of hearts. What is the probability that the remaining three cards will complete a full house? Answer to the nearest 0.01%.

[A full house is a poker hand of three of a kind and a pair.]

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, February 28, 2018 at noon Pacific Time. I will post the answer shortly after.

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