In this letter, we propose a novel probabilistic repetition scheme for the uplink massive MIMO system with grant-free access. Compared with canonical K-repetition, the proposed scheme is more flexible and covers the K-repetition as a special case. With the consideration of multiple practical factors, including the sporadic arrivals, the short-packet transmissions, probabilistic repetition, and channel estimation error, the reliability and throughput of the proposed probabilistic repetition assisted grant-free access scheme are theoretically analyzed. It is also proved that the optimal transmission probability for reliability maximization exists and can be found through gradient descent method. Simulation results validate the accuracy of our theoretical analysis, and also show that the proposed Optimal Probabilistic Repetition assisted grant-free Access scheme (OPRA) is superior to the popular modern grant-free random access with repetition transmission, that is, irregular repetition slotted ALOHA (IRSA).