Arthur Lupton's bishop problem

Twelve bishops go into an important conclave, but each hands his mitre to an attendant, who later assembles all the mitres on a table in the entrance hall.

The meeting continues until after dusk, and the attendant goes home, taking with him the key to the box containing the light switches. The bishops have to reclaim their mitres in the half light in which the mitres all look identical.

What is the probability that no bishop gets the correct mitre?