Aeroplane Probability Puzzle

People are waiting in line to board a 100-seat airplane. Steve is the first person in the line. He gets on the plane but suddenly can’t remember what his seat number is, so he picks a seat at random. After that, each person who gets on the plane sits in their assigned seat if it’s available, otherwise they will choose an open seat at random to sit in.

 
The flight is full and you are last in line. What is the probability that you get to sit in your assigned seat?

It's 1/2. Shocked? Read how!