It has been shown that ultrasonic techniques work well for online measuring of circumferential oil film thickness profile in journal bearings; unfortunately, they can be limited by their measuring range and unable to capture details of the film all around the bearing circumference. Attempts to model the film thickness over the full range of the bearing rely on deterministic approaches, which assume the observations to be true with absolute certainty. Unaccounted uncertainties of the film thickness may lead to a cascade of inaccurate predictions for subsequent calculations of hydrodynamic parameters. In the present work, a probabilistic framework is proposed to model the film thickness with Gaussian Processes. The results are then used to estimate the location of the bearing shaft under various operational conditions. A further step in the process involves using the newly-constructed dataset to generate likelihood maps displaying the probable location of the shaft centre, given the bearing rotational speed and applied static load. The results offer the possibility to visualise the confidence of the predictions and allow the true location to be found within an area of high probability within the bearing's bore.