In this paper, the authors propose a new formalization of the classical probability-possibility relation, which is further confirmed as a much complex, but natural provability – reachability – possibility – probability – fuzzy membership – integrability interconnection. Searching for the right context in which this relation can be consistently expressed for the particular case of experimentally obtained iris recognition results brought them to a natural (canonic) and universal fuzzification procedure available for an entire class of continuous distributions, to a confluence point of statistics, classical logic, modal logic, fuzzy logic, system theory, measure theory and topology.