An employer is about to hire one new employee from a group of N candidates, whose future potential can be rated on a scale from 1 to N. The employer proceeds according to the following rules:

(a) Each candidate is seen in succession (in random order) and a decision is made whether to hire the candidate.

(b) Having rejected m-1 candidates (m>1), the employer can hire the mth candidate only if the mth candidate is better than the previous m-1.

Suppose a candidate is hired on the i th trial. What is the probability that the best candidate was hired.