*Find the probability density for the distance from an event to its nearest neighbor for a Poisson process in three-dimensional space.*

All my book says about "Poisson processes" is

"The Poisson distribution often arises from a model called a

**Poisson process**for the distribution of random events in a set \(S\), which is typically one-, two-, or three-dimensional, corresponding to time, a plane, or a volume of space. Basically, this model states the if \(S_1,S_2,\ldots,S_n\) are disjoint subsets of \(S\), then the numbers of events in these subsets, \(N_1,N_2,\ldots,N_n\), are independent random variables that follow Poisson distributions with parameters \(\lambda|S_1|,\lambda|S_2|,\ldots,\lambda|S_n|\), where \(|S_i|\) denotes the measure of \(S_i\)."