Positronium (Ps) is widely used as a probe for studying nanometric porosities in condensed matter. Accessible experimental measurements concern annihilation rates by pickoff processes and contact densities (the electron density at the positron position). Existing models for describing Ps properties in small cavities do not justify the lowering of the contact density with respect to that of Ps in vacuum, as found in most materials. We formulate a two-particle model in which only the electron is confined in the cavity, while the positron is moving freely and feels the medium via a positive work function. Our calculation fully explains experimental data for a large class of materials and suggests a way to gain information on pore sizes and positron work functions.