I don't think it's quite as simple as the other answer claims. While it is true that the largest element will always be sorted, if the largest element is not first in the original list, there will be sorting performed prior to reaching the largest element.

After one iteration, the largest or smallest element is sorted depending on whether we sort in ascending or descending order. This means there are (n-1)! possible arrangements. Of these, only 1 arrangement represents the sorted array. So the probability of the array being sorted is 1/(n-1)!