Area-wide measurements of traffic flows are usually not possible with today's common sensor technologies. However, such information is essential for (urban) traffic planning and control. Hence, in order to support traffic managers, this paper analyses an approach for deriving traffic flows from probe vehicle speeds, which are potentially available with a wide spatial coverage, by looking at the speed-flow relationship as known from macroscopic traffic flow theory. In this context, it proposes a stochastic representation of the fundamental diagram via Bayesian networks which also involves the temporal dependencies between the observed traffic variables. By that, better results for traffic flow estimation from probe vehicle data (PVD) are obtained than by applying traditionally fitted deterministic curves of the speed-flow function. The paper describes the relevant theoretical concepts as well as the findings of an extensive validation using real-world PVD from about 4,300 taxis in Berlin, Germany.