Riddle of 100 Passengers

Here is a riddle, that I came across recently. Enjoy!

There are a hundred passengers to board a plane with a hundred seats. Each passenger has a ticket with number from 1 to 100 and enters the plane in this order. The first passenger sits on seat 1, and the second sits on seat 2 and so on. However, the first passenger, instead of using his seat, chooses a random seat of the available 100. The second passenger comes in and sits in its seat, if it is available, otherwise chooses randomly from the 99 free seats. Third passenger sits in seat 3, if it is free, otherwise chooses a random seat from the remaining 98, etc. What is the probability that 100th passenger sits in the 100th seat?