The retrieval of the 3D pose and shape of objects from images is an ill-posed problem. A common way to object reconstruction is to match entities such as keypoints, edges, or contours of a deformable 3D model, used as shape prior, to their corresponding entities inferred from the image. However, such approaches are highly sensitive to model initialisation, imprecise keypoint localisations and/or illumination conditions. In this paper, we present a probabilistic approach for shape-aware 3D vehicle reconstruction from stereo images that leverages the outputs of a novel multi-task CNN. Specifically, we train a CNN that outputs probability distributions for the vehicle's orientation and for both, vehicle keypoints and wireframe edges. Together with 3D stereo information we integrate the predicted distributions into a common probabilistic framework. We believe that the CNN-based detection of wireframe edges reduces the sensitivity to illumination conditions and object contrast and that using the raw probability maps instead of inferring keypoint positions reduces the sensitivity to keypoint localisation errors. We show that our method achieves state-of-the-art results, evaluating our method on the challenging KITTI benchmark and on our own new 'Stereo-Vehicle' dataset.