The estimation of the free flow speed (FFS) distribution is important for capacity analysis, determination of the level-of-service, and setting speed limits. Subjective time headway thresholds have been commonly used to identify vehicles travelling under free flow speed conditions i.e., vehicles whose speeds are not influenced by the vehicle in front. Since, the headway a driver operates under the free flow state is subjective and varies from driver to driver, such approaches can introduce biases in the FFS estimation. Therefore, in this paper a parametric probabilistic latent approach is proposed based on discrete choice utility theory to estimate the FFS distribution on urban roads and simultaneously the probability that drivers perceive their state as constrained by the vehicle in front. This methodology is used to estimate the impacts of road characteristics and Posted Speed Limit (PSL) changes on the FFS distribution using an extensive dataset of speed observations from urban roads with varying characteristics. The results show that the simultaneous estimation of the free flow speed distribution and the state the driver is in (e.g., free or constrained) is feasible. The analysis indicates that the FFS is influenced by several road characteristics such as land use, on-street parking and the presence of sidewalks. The PSL change impacts not only the distribution of the free flow vehicles but also the speed distribution of the constrained vehicles. The constrained probabilities vary depending on the PSL change with higher probabilities for lower speed limits.