A normal deck of 52 playing cards is well shuffled and then 4 cards are dealt to Ann and 4 cards ar dealt to Bob. Ann looks at her c that all 4 of them are from the same suit, that suit being hearts. She is interested in the probability that Bob also has 4 cards that belong to a single suit, allowing for her knowledge of the cards she holds.
Please correct my answer if it is incorrect: $$\text{Probability}=P(\text{Bob has all hearts} |\text{Ann has all hearts})+P(\text{Bob has all clubs/spades/diamonds}|\text{Ann has all hearts})$$
$$=\frac{\binom{9}{4}}{\binom{48}{4}}+\frac{\binom{3}{1}\times\binom{13}{4}}{\binom{48}{4}}$$
$$=\frac{757}{64860}$$
I am aware that this is a conditional probability, but I was unsure how to apply Bayes' Theorem in this scenario.