order statistics/life testing problem

I would need to practice the following type of problem. I have a
sample of n independent random
vars. I fix one of the order statistics. What is the joint
distribution of the remaining?

I transcribed an example problem below.
5 people take a test. When 3 people are finished, the exam is halted.
Those 3 students turn in their work. How much longer will the
remaining students take? In other words: given the time at which the
median is observed, what is the additional life left for the remaining
two?

Your help is much appreciated. Your pointers are welcome too.

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