The need for intelligent and efficient resource provisioning for the productive management of resources in real-world scenarios is growing with the evolution of telecommunications towards the 6G era. Technologies such as Open Radio Access Network (O-RAN) can help to build interoperable solutions for the management of complex systems. Probabilistic forecasting, in contrast to deterministic single-point estimators, can offer a different approach to resource allocation by quantifying the uncertainty of the generated predictions. This paper examines the cloud-native aspects of O-RAN together with the radio App (rApp) deployment options. The integration of probabilistic forecasting techniques as a rApp in O-RAN is also emphasized, along with case studies of real-world applications. Through a comparative analysis of forecasting models using the error metric, we show the advantages of Deep Autoregressive Recurrent network (DeepAR) over other deterministic probabilistic estimators. Furthermore, the simplicity of Simple-Feed-Forward (SFF) leads to a fast runtime but does not capture the temporal dependencies of the input data. Finally, we present some aspects related to the practical applicability of cloud-native O-RAN with probabilistic forecasting.