[math-fun] "Random" Deck?

Recently, my daughter asked the following question: After shuffling an ordinary deck of cards, what is the probability of having none of the cards in their proper place with respect to rank only? That is, ace through king, ace through king, etc. (four times). In this problem the suit of each card does not matter. Any help or direction to a reference would be appreciated. Thank you. R. Wainwright