2009 passengers are waiting in a line to board an airplane with 2009 seats. Each passenger has a boarding pass that has his/her seat number on it. The first passenger, however, was oblivious and chose a random seat to sit on.
For each subsequent passenger, he/she will try to sit on his/her assigned seat first. If that seat is taken by someone else, he/she will choose a random empty seat to sit on.
What is the probability that the last passenger would sit on his assigned seat?