Why is it more likely that exactly one cross over will take place?

Hello. I'm studying genetic linkage and the recombination frequency calculation (that is assumed to be directly proportional to allele distance) considers that only one cross over will take place. I know this is an estimation, but I want to know what the biological mechanism is that justify the probability that EXACTLY ONE crossover will take place.
In other words, what is the probability of no cross overs taking place, or a double cross over, or a triple cross over, and why are these probabilities lower than for a single crossover? And also, it is considered that all regions in the chromosome have the same chance to suffer a cross over, is this correct? If not, what are the most probable and the least probable sites and why?