I had a discussion with a friend the other day:

Deck of cards (52 cards). 13 of them are hearts. Well shuffled, randomly dealt.

Situation 1

I'm sitting at a tableby myselfwith 2 cards in my hands. Both are hearts.

The rest of the deck is on the table.

X = The probability that the top card of the remaining deck, when turned, is a heart.

Situation 2

I'm sitting at a tabletogether with 4 other peoplewe all have 2 cards in our hands. I do not know which cards are held by the other players. Both my cards are hearts.

The rest of the deck is on the table.

Y = The probability that the top card of the remaining deck, when turned, is a heart.

Question

X = Y ?

And why / why not?