The disturbances caused by the blood flow and tissue surface motions are major concerns during the motion planning of a intracardiac robotic catheter. Maintaining a stable and safe contact on the desired ablation point is essential for achieving effective lesions during the ablation procedure. In this paper, a probabilistic formulation of the contact stability and the contact safety for intravascular cardiac catheters under the blood flow and surface motion disturbances is presented. Probabilistic contact stability and contact safety metrics, employing a sample based representation of the blood flow velocity distribution and the heart motion trajectory, are introduced. Finally, the contact stability and safety for a MRI-actuated robotic catheter under main pulmonary artery blood flow disturbances and left ventricle surface motion disturbances are analyzed in simulation as example scenarios.