Since the important work on reasoning under uncertainty by Kahneman and Tversky in the 1970s, the description of how people think about probability by using intuitions, conceptions and misconceptions have been studied in psychology and mathematics education. Over the years, the body of the literature have identified and studied many of them. Some conceptions, such as representativeness and availability, are well known. But not all of the conceptions have been studied many times and the conceptions presented in the literature usually don't relate them to each other. Therefore, it is now difficult to have a broader perspective on people conceptions of probability. In addition to that, some epistemological differences exist between the conceptions. Not all of them use the same kind of reasoning for addressing different aspects of probability. Thus, a broader perspective of people conceptions of probability involves not only knowing about conceptions and links them together; it also includes knowing about the mathematical aspect involved.This chapter will define what a conception is and present a classification of some of them given in the literature, based on their epistemological differences.