One king, queen and jack before the two of hearts

A well-shuffled deck is dealt face up one card at a time until the two of hearts turns up. Find the probability that, before it appears, exactly one king, exactly one queen and exactly one jack have been dealt.

$\tfrac{16}{715}$. Only the relative order of the $13$ relevant cards (the four kings, four queens, four jacks and the two of hearts) matters. The first four of them must be one king, one queen and one jack in any order and then the two of hearts: $3!\cdot 4^3=384$ favourable sequences out of $17160$ equally likely ones.