The use of massive multiple-input multiple-output (MIMO) to serve a crowd of user equipments (UEs) is challenged by the deficit of pilots. Assuming that the UEs are intermittently active, this problem can be addressed by a shared access to the pilots and a suitable random access (RA) protocol. The strongest-user collision resolution (SUCRe) is a previously proposed RA protocol that often privileges the UEs closer to the base station (BS). In contrast, we propose a novel RA protocol using a decentralized pilot power allocation method that aims at a fairer performance. The proposed access class barring with power control (ACBPC) protocol allows each UE to estimate, without additional overhead, how many UEs collided for the chosen pilot and calculate an ACB factor, which is then used to determine the pilot retransmission probability in the next protocol step. The results show that the proposed ACBPC protocol is superior to SUCRe in terms of providing a fair connectivity for very crowded networks, although still being distributed and uncoordinated as the original SUCRe protocol.