The prediction of remaining useful life (RUL) is crucial in the prognostics and health management (PHM) of rolling-element bearings, which serve a significant role in a wide range of rotating machinery. Effective RUL prediction techniques with uncertainty estimation facilitate predictive maintenance that optimises manufacturing efficiency and prevents unscheduled downtime. To assess the performance of probabilistic RUL prediction models, this paper presents a comparative study among state estimation methods based on Bayesian filters and a direct prediction method using deep neural networks. The first method employs the extended Kalman filter (EKF) for bearing degradation state estimation based on the envelope spectral indicator (ESI) that reflects the vibration intensity of defect frequencies in envelope spectra. The second prediction method compares the particle filter (PF) for bearing RUL prediction using the extracted ESI. In the third method, the nonlinearity between envelope spectra and bearing RUL is explored using probabilistic neural networks, where a supervised convolutional variational autoencoder for regression (CVAER) is used to predict RUL distributions. Using openly available run-to-failure vibration data from a bearing test rig, the model performances are evaluated regarding the accuracy of predicted RUL and the corresponding uncertainty interval across the bearing degradation stage.