How would I solve this statistics problem

on a deck of 52 cards, I was given two cards that is a "six of hearts" and "seven of hearts",

the dealer showed three cards, "two of hearts" "jack of diamond" and "king of hearts"

what is the probability that the next card is a "heart", or if not, the 2nd card pick is a "heart"

pls show solution... there are 13 heart cards in a deck

There are already 4 heart cards revealed and altogether 5 cards revealed. There are 47 cards left in the deck and 9 heart cards left. So 1st probability is 9/47. If the first card isn't a heart, there are 46 cards left and still 9 heart cards left, so 2nd probability is 9/46.

first draw: 6heart and 7heart - 11 heart cards left, 50 cards left

2nd draw: 2heart, Jdiamond and Kheart - 9 heart left, 47 cards left

3rd draw:
probability of a heart = 9/47

4th draw: 46 cards left with still 9 heart cards
probability of a heart = 9/46