Due to their very thin tunnel barrier layer, magnetic tunnel junctions show dielectric breakdown at voltages of the order of 1 V. At the moment of breakdown, a highly conductive short is formed in the barrier and is visible as a hot spot. The breakdown effect is investigated by means of voltage ramp experiments on a series of nominally identical Co/Al2O3/Co tunnel junctions. The results are described in terms of a voltage dependent breakdown probability, and are further analyzed within the framework of a general model for the breakdown probability in dielectric materials, within which it is assumed that at any time the breakdown probability is independent of the (possibly time-dependent) voltage that has been previously applied. The experimental data can be described by several specific forms of the voltage breakdown probability function. A comparison with the models commonly used for describing thin film SiO2 breakdown is given, as well as suggestions for future experiments.