Punctuality is a key performance indicator for any airline. Hub-and-spoke airlines are particularly committed to on-time arrivals to guarantee passenger connections. Flights that are delayed at departure need to compensate for the lost time whilst airborne. Because fueling takes place well before scheduled departure, predicted departure delays determine the planned fuel amounts for en-route speed optimization. To prevent unnecessary fuel burn, airlines benefit from highly accurate departure delay predictions. This study aims to extend previous work on airline departure delay forecasting to a dynamic and probabilistic domain, whilst incorporating novel day-of-operations airline information to further minimize prediction errors. Random Forest, CatBoost, and Deep Neural Network models were proposed for a case study on KLM departures from Amsterdam Airport Schiphol between 1 January 2020 and 1 August 2023. The Random Forest model was selected for its superior probabilistic performance and high accuracy in predicting delays between 5 and 25 minutes, for which en-route speed optimization has the largest effect. The departure delay probability distribution forecasts are made at six distinct prediction moments: 90, 75, 60, 45, 30, and 15 minutes before scheduled departure time. At the 90-minute prediction horizon, the model reaches a Mean Absolute Error (MAE) of 8.46 minutes and a Root Mean Square Error (RMSE) of 11.91 minutes. Simultaneously, for 76% of flights, the actual delay is within the predicted probability distribution range. Considering the costs and emissions associated with the decision-making following the departure delay prediction model, this study puts strong emphasis on explainability. Flight dispatchers are therefore provided not only the predicted departure delay but also the main factors impacting the prediction, explaining the context of the flight. The versatility of the model was demonstrated in two shadow runs, where delays caused by familiar and unfamiliar factors were successfully predicted.