Last queen before last king given an early pattern

A standard $52$-card deck is shuffled. Eve will win $100 if the final queen in the deck comes before the final king. Her friend looks through the deck and tells her that exactly two queens come before the first king. With this information, what are Eve's expected winnings?

$60. Only the relative order of the $8$ kings and queens matters, and all orders are equally likely. The hint fixes the first three as queen, queen, king, leaving $2$ queens and $3$ kings in random order; Eve wins iff the last of these is a king, probability $\tfrac35$.