Several initiatives are being developed to shift the current paradigm in Air Traffic Management (ATM) from the tactical-based approach to more strategic-based coordination of flights. This transformation of the ATM system relies on the improvement of predictive models that predict the 4D-trajectory of an aircraft. Previous studies primarily applied deterministic models that compute a single predicted trajectory. These models were assessed on their predictive accuracy. However, the accuracy of the predictions is highly impacted by uncertainties that affect the progression of a flight. These uncertainties are commonly related to the lack of detailed information concerning the flight intent, or the inaccuracy of positional and weather-related data. This study applied two probabilistic techniques: the model-based particle filtering model and the data-driven Gaussian Process Regression. Both approaches model the uncertainties and provide a predictive distribution of trajectories that allows for the evaluation of both the accuracy and the uncertainty of the predictions. These models were applied to predict the descent trajectories of aircraft arriving at Amsterdam Airport Schiphol. The results showed that the uncertainty of the predictions could be reduced by incorporating flight-plan data and meteorological data in the predictive models. Also, the accuracy was improved which demonstrates the importance of these sources of data in the predictions of aircraft trajectories. The proposed models have been able to quantify the uncertainty in trajectory predictions that could be used to further develop and improve the management and prediction of 4D-trajectories.