Card following an ace that first appears at position 27

A standard deck is shuffled and dealt face up from the top. It turns out that the first ace is the $27$th card. Given this, what is the probability that the $28$th card is the two of hearts?

$\tfrac{11}{600}$. Given the condition, the first 26 cards are a random set of 26 of the 48 non-aces, so the two of hearts is among the remaining cards with probability $\tfrac{22}{48}$. Those 25 remaining cards are in random order, so it sits in position 28 with probability $\tfrac1{25}$: $\tfrac{22}{48}\cdot\tfrac1{25}=\tfrac{11}{600}$.