It takes t amount of time for you to navigate the Gauntlet of Pain. The Gauntlet electrifies and shocks anyone on it at random intervals. The intervals between shocks are independently and identically distributed (think Poisson). Obviously, you do not wish to be shocked. Assume shocks are instantaneous. Picture an "opportunity" as a window of time (an interval) that allows you to make it across the Gauntlet without being shocked. Suppose the initial window begins directly after the last shock (shock number 0).

What is the probability that the first opportunity occurs just before the nth shock?

What is the probability that you will have x number of opportunities before the nth shock?

Combining the information above, find the probability that the xth opportunity is a close call (that it occurs immediately before the nth shock).