Regional air quality monitoring, a critical component of sustainable development is realized through various air quality observation stations established across a region. Accurate forecasting of air quality data collected from these observation stations requires the modelling of spatial-temporal patterns in the data. Deep learning algorithms, known for their ability to capture layers of abstraction, can proficiently achieve spatial-temporal modeling. However, deterministic models that produces point forecast does not consider the underlying model uncertainty during prediction and are therefore less reliable for real-time applications. Probabilistic forecasting models that forecast prediction intervals rather than point estimates can overcome this through uncertainty quantification. The objective of the proposed study is three-fold: i) develop an efficient deterministic deep learning spatial-temporal neural network named DL-STNN for spatial-temporal air quality forecasting; ii) investigate different approaches to uncertainty quantification in deep learning models and integrate some of them, such as Monte-Carlo Dropout, Ensemble Averaging, Gaussian Process Regression, Quantile Regression, and Bayesian Inference, in tandem with DL-STNN to facilitate probabilistic forecasting; and iii) evaluate the developed deterministic and probabilistic models, using a real-world Delhi air quality dataset. The evaluation results show that, among the deterministic models, DL-STNN outperforms the baselines with 39.8% more accurate predictions and performs consistently across all seasons in Delhi. Furthermore, among the DL-STNN-based tandem models that performed probabilistic forecasting, Bayesian DL-STNN proved efficient. It does 13% more accurate point forecasting and has 20% higher suitability score than the other tandem models, indicating that Bayesian inference adapts DL-STNN more reliable for real-time applications.