Psychological research on eyewitness testimony has made important contributions to the measurement of lineup fairness. The mock witness task, and measures of functional size, effective size, and diagnosticity have proved useful both in application to real-world problems and to ongoing research aimed at the optimization of criminal investigation techniques. However; these measures are typically used in the absence of any inferential statistical considerations. This is unfortunate, since the mock witness task relies on an implicit probability model. An attempt is made in this paper to identify a suitable formal probability model for the mock witness task, and suggestions are made with respect to how to reason inferentially about many of the lineup measures developed in psycholegal research. It is important to reason inferentially about these measures, and a failure to do so may mislead those to whom measures of lineup fairness are presented.