the difficulty with this arises when the event "b" is too small to have a non-zero probability. for example, suppose we have a random variable "x" with a uniform distribution on formula_2 and "b" is the event that formula_3 clearly, the probability of "b," in this case, is formula_4 but nonetheless we would still like to assign meaning to a conditional probability such as formula_5 to do so rigorously requires the definition of a regular conditional probability.