Measurements do not result in an exact value of the measured quantity; even after the most accurate measurement, there is still some uncertainty about the actual value of the measured quantity. Traditionally, in science and engineering, this uncertainty is characterized by a probability distribution; however, often, we do not know this probability distribution exactly. So, to get a more adequate description of this uncertainty, we must consider classes of possible probability distributions. A natural question is: Are all possible classes needed for this description? In this paper, we show that even for simple situations, we indeed need arbitrary closed convex classes of probability distributions.