In one embodiment, a device obtains telemetry data regarding an encrypted traffic session in a network. The telemetry data includes Transport Layer Security (TLS) features of the traffic session and auxiliary information indicative of a destination address of the traffic session, a destination port of the traffic session, or a server name associated with the traffic session. The device retrieves, using the obtained telemetry data, a plurality of candidate processes from a TLS fingerprint database that relates processes with telemetry data from encrypted traffic sessions initiated by those processes. The device uses a probabilistic model to assign probabilities to each of the plurality of candidate processes. The device identifies one of the plurality of candidate processes as having initiated the encrypted traffic session based on its assigned probability.