If the drunk somehow chooses his correct seat, the probability is 100% as everyone else will find their correct seat. However, if the drunk does not, everyone who has a correct seat still will find their seat accept for the one person who's seat has been taken by the drunk, in which case he will take the remaining seat that the drunk left behind. He either gets the correct seat or he doesn't... 50%.
That's somewhat what I said...although, if the second person to enter is the owner of the seat that the drunk took, they will sit in a random seat. If the third person to enter is the owner of the seat that the second person sits in, he too will sit somewhere else. Either way, the last person has a 50% (or 1/2) chance of getting his seat.
What I did originally, was make up a random number of seats (50), and I sat the drunk in seat one (and made his seat, seat #50). And I simply put the second person (who's seat was seat #1), in seat 2. If this pattern continued, the last person would not be able to sit in their seat (seat 49, because they will be left to sit in seat 50, the drunk's seat.) But that's only if the pattern continues, if say the second to last person sits in seat 50 instead of 49, then the last person to enter is free to take their own seat.
So no matter how you look at it (unless the drunk takes his own seat), it's a 50% or 1/2, chance.
of course, you could just assume that there are only three seats (3 people).
The drunk is asisgned to seat #1, the second person, seat #2, and the last #3.
The drunk sits in seat #2: the second person either sits in seat #1 or #3 (which leaves the last person with whatever's left (could be his seat, or not)
The drunk sits in seat #3: the second person sits in his own seat, seat #2, and the last person is forced into the first seat. (in this case, the outcome is 100% that he will sit in the wrong seat.)
So, I guess it's not exactly 50%...hmm. does that mean that the odds are about 1/3 that he will sit in his correct seat?
or...is it a...3/2 chance...? No that doesn't make sense either...agh! This is much more complicated than I thought it would be...
The answer is: it's either 50% or 0%. There isn't one correct answer.
(I'll make diagrams if I must.)