Sock-dresser search

You left your socks somewhere in your room. You think there’s a ⁴⁄₅ chance that they’re in your dresser, so you start looking through your dresser’s 8 drawers. After checking 6 drawers at random, you haven’t found your socks yet. What is the probability you will find your socks in the next drawer you check?

You’re encouraged to solve the problem yourself before looking up the answer. The answer can be found in Belief revision as probability elimination.