Two Decks, Fifteen Cards Lost

Two identical standard decks are shuffled together into one stack of 104 cards, so the stack holds exactly two copies of each of the 52 rank-suit kinds (two aces of spades, two sevens of hearts, and so on).

Fifteen cards fall out of the stack, chosen uniformly at random from the 104. The 89 cards left over still contain one complete standard deck exactly when no kind lost both of its copies.

What is the probability of that? Answer format: round to 3 decimal places.