In this paper we present a new similarity measure between possibility distributions based on the Kullback-Leilbler divergence in the domain of real numbers. The possibility distributions are obtained thanks to a previously proposed probability-possibility transformation lying on the principle that a possibility measure can encode a family of probability measures. We consider here two particular possibility distributions build from parameter estimation of the Weibull and Rayleigh probability laws. The analytical expression of the KL divergence for the two considered possibility distributions are given, allowing a simple computation which depends on the parameters of the possibility distribution obtained. This new similarity measure is compared to the existing KL divergence for probability distributions in a context of change detection over simulated images as they provide a ground-truth of the changes required to evaluate the rate of true detection against false alarm.