Zeke is the janitor at the Alphabet Soup Works, which employs 26 people. The employee parking lot has 26 numbered spaces, and each employee is assigned a single spot. Each employee is generally very careful to park in their own spot, but if that spot has been taken for some reason, the employee will choose another spot at random in the parking lot.
This morning, Alfred was the first to arrive at work; because of a crazy party last night, he had a terrible headache, and when he got to the parking lot, he didn't bother to try to park in his own spot; he simply parked at random. Of course, as other employees arrived that morning, they had to do the best they could, taking their own assigned spots if possible, and otherwise picking one of the remaining spaces at random.
Zeke is the last of the employees to arrive at work that morning. There is a single space left in the lot. What are the chances that this empty space is actually Zeke's assigned spot?
I give up, show me the solution.