We present a method to implement probabilistic treatment planning of intensity-modulated radiation therapy using custom software plugins in a commercial treatment planning system. Our method avoids the definition of safety-margins by directly including the effect of geometrical uncertainties during optimization when objective functions are evaluated. Because the shape of the resulting dose distribution implicitly defines the robustness of the plan, the optimizer has much more flexibility than with a margin-based approach. We expect that this added flexibility helps to automatically strike a better balance between target coverage and dose reduction for surrounding healthy tissue, especially for cases where the planning target volume overlaps organs at risk. Prostate cancer treatment planning was chosen to develop our method, including a novel technique to include rotational uncertainties. Based on population statistics, translations and rotations are simulated independently following a marker-based IGRT correction strategy. The effects of random and systematic errors are incorporated by first blurring and then shifting the dose distribution with respect to the clinical target volume. For simplicity and efficiency, dose-shift invariance and a rigid-body approximation are assumed. Three prostate cases were replanned using our probabilistic objective functions. To compare clinical and probabilistic plans, an evaluation tool was used that explicitly incorporates geometric uncertainties using Monte-Carlo methods. The new plans achieved similar or better dose distributions than the original clinical plans in terms of expected target coverage and rectum wall sparing. Plan optimization times were only about a factor of two higher than in the original clinical system. In conclusion, we have developed a practical planning tool that enables margin-less probability-based treatment planning with acceptable planning times, achieving the first system that is feasible for clinical implementation.