In this paper, a successive interference cancellation (SIC) aided K-repetition scheme is proposed to support contention-based mission-critical machine-type communication (MTC) in cell-free (CF) massive multiple-input and multipleoutput (MIMO) systems. With the assistance of a tailored deep neural network (DNN) based preamble multiplicity estimator, the proposed SIC in K-repetition is capable of fully cancelling the interference signals, which leads to the reliability improvement in CF massive MIMO. Simulation results show the accuracy of preamble multiplicity estimation by the proposed DNN, and demonstrate that, compared to the existing schemes, the proposed SIC scheme can achieve an improvement of two orders of magnitude in terms of block error rate (BLER) under a given latency constraint. Moreover, when the number of access points (APs) is sufficiently large, employing the proposed SIC scheme provides a great potential to meet ultra-reliable and low-latency requirements, e.g., 10-5 BLER and 1 ms access latency, for crowd mission-critical applications, which is far beyond the capabilities of the existing schemes.