The probability of a probability is a difficult concept to grasp, especially when dealing with continuous values. The key is to focus on ranges of values and think of the area of each range as representing the probability density. The probability density function (PDF) is used to find the probability of a random variable lying between two values by calculating the area under the curve between those values. The rules for combining probabilities of different sets are different in continuous settings, and measure theory is used to make rigorous the idea of associating numbers like probabilities to various subsets of all possibilities.