Question: Quantitative Puzzle

I came across a quite interesting problem as seen below  (and no it is not homework.)

I am just interested in how such a problem would be solved ?!

"A student association organises a large-scale dinner for 128 students. The chairs are
numbered 1 through 128. The students are also assigned a number between 1 and 128.
As the students come into the room one by one, they must sit at their assigned seat.
However, 1 of the students is so drunk that he can’t find his seat and takes an arbitrary
one. Any sober student who comes in and finds his seat taken also takes an arbitrary
one. The drunken student is one of the first 64 students. What is the probability that the
last student gets to sit in the chair assigned to him? "