Probability that ace of spades is at bottom of deck IF ace of hearts is NOT at top 
What is the probability that the ace of spades is at the bottom of a standard deck of 52 cards given that the ace of hearts is not at the top?

I asked my older brother, and he said it should be $\frac{50}{51} \cdot \frac{1}{51}$ because that's $$\mathbb{P}(A\heartsuit \text{ not at top}) \times \mathbb{P}(A\spadesuit \text{ at bottom}),$$ but I'm not sure if I agree. Shouldn't the $\frac{50}{51}$ be $\frac{50}{52}$?
Thanks you!

The ace of hearts has 51 positions available (since it's not at the top).
Having placed it somewhere, there are 51 positions available for ace of spades, so
Pr = P(ace of spades not at bottom)*P(ace of diamonds at bottom)
= 50/51 *1/51 = 50/51² 
