There are 100 seats in an airplane.

There are 99 male passangers with reserved seats and one female passager that does not have a ticket.

The female passanger enters the plane first, selects a random seat (out of the total 100 seats) and sits in it.

Then the first man enters. If his seat is not taken, he sits in it. If it is taken, he selects a non-occupied random seat in the plane and sits there.

The rest of the men enter and do the same - each of them first tries to take their own seat (if it is available) and otherwise sits in a random non-occupied seat.

What is the probability that the last man to enter the plane gets their original seat?