Modern footbridges are very slender structures, often characterized by natural frequencies within the range of the dominant walking harmonics; thus, they can be very sensitive to walking-induced vibrations. In the present paper, real pedestrian traffic conditions are modeled probabilistically, considering several sources of randomness among which pedestrian arrivals, walking frequencies and velocities, force amplitudes and pedestrian weights. Based on such a probabilistic model, the dynamic response to streams of pedestrians is analyzed through a spectral approach, introducing suitable models for the power spectral density function and for the coherence function of pedestrian-induced forces, considered as a stationary random process. Thus, footbridges vibration serviceability analysis is tackled with the classical methods of linear random dynamics and the maximum dynamic response is determined in closed-form. A discussion about the choice of scenarios to be studied for footbridge serviceability analyses appears fundamental in order to validate the possibility of technically using a spectral approach like the one here proposed.