The use of borehole fluid injections is typical for exploration and development of hydrocarbon or geothermal reservoirs. Such injections often induce small-magnitude earthquakes. The nature of processes leading to triggering of such microseismicity is still not completely understood. Here, we consider induced microseismicity, using as examples two case studies of geothermal reservoirs in crystalline rocks and one case study of a tight-gas sandstone reservoir. In all three cases, we found that the probability of induced earthquakes occurring is very well described by the relaxation law of pressure perturbation in fluids filling the pore space in rocks. This strongly supports the hypothesis of seismicity triggered by pore pressure. Moreover, this opens additional possibilities of using passive seismic monitoring to characterize hydraulic properties of rocks on the reservoir scale with high precision.