This paper deals with a possibilistic expression of uncertainty that consists in representing measurements by a family of confidence intervals stacked atop one another. In fact, this approach defines the upper bound of the probability distributions consistent with these confidence intervals. Applying the proposed transformation to a uniform probability distribution, the result is a triangular possibility distribution. Moreover, it is shown that this triangular possibility distribution is an upper bound of any possibility distribution equivalent (in the above sense) to a probability distribution bounded by the support of the triangle. Bridges with the weil-known probability inequalities of Bienaymé-Chebychev and Camp-Meidel are also established. Keywords : uncertainty, possibility theory, probability theory.