We consider the problem of fairly allocating a set of <math>m</math> indivisible objects to <math>n</math> agents having additive preferences over them. In this paper we propose an extension of this classical problem, where each object can possibly be in bad condition (<i>e.g</i> broken), in which case its actual value is zero. We assume that the central authority in charge of allocating the objects does not know beforehand the objects conditions, but only has probabilistic information. The aim of this work is to propose a formal model of this problem, to adapt some classical fairness criteria to this extended setting, and to introduce several approaches to compute optimal allocations for small instances as well as suboptimal good allocations for real-world inspired allocation problems of realistic size.