Factorial ratio sum of finite series

Question

Given: $ S = \sum_{i=1}^{n-1}{i! \over n!} $

How would I find the sum for an arbitrarily large $n$ ?

Example: $n=5$

$ S = \frac{1!}{5!} + \frac{2!}{5!} + \frac{3!}{5!} + \frac{4!}{5!} = 0.275 $