[SOLVED] Probability question

Here's my problem.

You are the** last** person to arrive to the event with k numbered seats

(say, k >= 2), and all k-1 seats have been already randomly taken. You

insist on sitting in the seat printed on your ticket, so you find your

seat and (if it's not empty), you make the person sitting there stand up

and find her own seat. That person in turn finds her own seat and makes

the person sitting there stand up, etc... The process continues until

someone finally seats in the empty seat. The question is, what's the

probability that the **first** person to arrive to the event will not have

to stand up?

Appreciate all your help