Driving energy consumption plays an important role in the navigation of autonomous mobile robots in off-road scenarios. However, the accuracy of the driving energy predictions is often affected by a high degree of uncertainty due to unknown and constantly varying terrain properties, and the complex wheel-terrain interaction in unstructured terrains. In this paper, we propose a probabilistic deep meta-learning approach to model the existing uncertainty in the driving energy consumption and efficiently adapt the probabilistic predictions based on a small number of local measurements. Our method expands upon an existing deterministic deep-meta learning model that, in contrast, only provided single-point energy estimates. The performance of our method is compared against the deterministic approach in a 3D-body dynamic simulator over several typologies of deformable terrains and unstructured geometries. In this way, we provide evidence of the benefit of the proposed method to enhance the predictions with informative probabilistic considerations, which can be crucial to the safety of mobile robots traversing challenging, unstructured environments.