## Probability changes each event

Hi,

I have a problem with choosing mulitple paths. Let's say you are on top of the hill and have n-paths leading down. Each have the same probability (1/n). You choose one, and the choosen path becomes "more" visible than others. Now N people go down this hill. What is the end result?

I have made computer simulation for solving this problem, but I would like to know if there is any analitical solution I could use here.

Thanks,

Toml