We present a novel approach to motion planning for autonomous ground vehicles by formulating motion primitives as probabilistic distributions of trajectories (aka probabilistic motion primitives - ProMP) and performing stochastic optimisation on them for finding an optimal path. We show that compared to the traditional approach of using discrete motion primitives or direct stochastic optimisation of the whole path; incorporating ProMPs enables higher quality of paths by enabling constraint conditioning; combination and blending of probability distributions. We present two motion planners utilizing this approach: feasibility-based trajectory sampling (PROMPT-S) and stochastic gradient-based trajectory optimisation (PROMPT-O). We show simulation results of our approach outperforming state-of-the-art optimisation as well as discrete motion primitives-based planners. We additionally illustrate the versatility of our approach by showing PROMPT's ability to handle significantly skewed motion primitives; e.g; as induced by steering failure in AGVs as well as the composition of motion primitives to perform complex maneuvers. Finally; we demonstrate the practicality of these planners by implementing them on a real self-driving vehicle navigating on structured and unstructured off-road terrains.