Plane Stupid

There are 100 passengers boarding a 100 passenger airplane. Passenger 1 should sit in seat 1, passenger 2 in seat 2, and so forth. When passenger 1 gets onto the plane, he is disoriented, so he randomly picks a seat. Each of the remaining passengers (2, 3, 4, etc.) gets onto the plane and takes their seat if it is available or picks one of the remaining seats at random if it is not. (Passengers are not required to keep moving forward.)

What is the chance that the last passenger (passenger 100) will get his seat?