Here is the complete riddle image (click to enlarge)
Here is the trick: There is an open cycle of passengers sitting on random seats, simply because the first guy sat on a random sit. There is only one way that you will not sit on your seat: If one of these guys sits on your seat first!
Now suppose that one random passenger finds his seat taken and has to choose of another random sit: There are 3 possibilities:
1- He sits on your seat
2- He sits on the first guy's seat
3- He sits on any other seat
As you can see, the chances for cases 1 and 2 are exactly the same for all passengers that will have to chose a random seat. If one sits on the first guy's seat (2), then the random choosing cycle ends. If one sits on your seat, then you will lose your seat. At the end, one of the two scenarios will be true, and since they both have the same chance, then the chance for you to sit on your seat is 50%