The safety of the air transportation system is affected by a variety of uncertainties arising from multiple sources. This paper investigates a diagnosis and prognosis approach to detect anomalies in the flight trajectory, diagnose root causes, and then perform prognosis regarding the risk of occurrence of adverse events, in the presence of various sources of uncertainty. The proposed method is illustrated using a three-step procedure. First, using flight trajectory data, we evaluate the probabilities of system states corresponding to each failure case, from which we formulate a state-space model. Next, we perform anomaly detection for a specific flight trajectory by developing a Bayesian state estimation-based method, and subsequently identify the cause of the detected anomaly. Once the root cause is identified, prognosis is performed to predict the future state in a probabilistic manner. The proposed method is illustrated using near-ground landing data synthetically generated from an open source air traffic simulator - BlueSky. The simulation data mimicking the near-ground landing process with different initial states (e.g., aircraft altitude and speed, response delay, and brake performance) and other factors (such as wind direction) are used to demonstrate the procedures of diagnosis and prognosis.