Progressive filtering is a simple way to perform hierarchical classification, inspired by the behavior that most humans put into practice while attempting to categorize an item according to an underlying taxonomy. Each node of the taxonomy being associated with a different category, one may visualize the categorization process by looking at the item going downwards through all the nodes that accept it as belonging to the corresponding category. This paper is aimed at modeling the progressive filtering technique from a probabilistic perspective, in a hierarchical text categorization setting. As a result, the designer of a system based on progressive filtering should be facilitated in the task of devising, training, and testing it.