I got the following formula for finding the probability: (s-k-1 C n-k-1) * (m-1 C k) / (s-1 C n-1)

I calculated the above result using Bayes theorem:

P(Alice|k) = s-k-1 C n-k-1 / s-k C n-k

P(k) = (m-1 C k * s-k C n-k) / s C n

P(Alice) = s-1 C n-1 / s C n

P(k|Alice) = P(Alice|k) * P(k)/ P(Alice)

Can someone please point out the mistake?