Efficient resource management is critical for Non-Terrestrial Networks (NTNs) to provide consistent, high-quality service in remote and under-served regions. While traditional single-point prediction methods, such as Long-Short Term Memory (LSTM), have been used in terrestrial networks, they often fall short in NTNs due to the complexity of satellite dynamics, signal latency and coverage variability. Probabilistic forecasting, which quantifies the uncertainties of the predictions, is a robust alternative. In this paper, we evaluate the application of probabilistic forecasting techniques, in particular SFF, to NTN resource allocation scenarios. Our results show their effectiveness in predicting bandwidth and capacity requirements in different NTN segments of probabilistic forecasting compared to single-point prediction techniques such as LSTM. The results show the potential of black probabilistic forecasting models to provide accurate and reliable predictions and to quantify their uncertainty, making them indispensable for optimizing NTN resource allocation. At the end of the paper, we also present application scenarios and a standardization roadmap for the use of probabilistic forecasting in integrated Terrestrial Network (TN)-NTN environments.