Mobile edge computing (MEC) has been introduced to provide additional computing capabilities at network edges in order to improve performance of latency critical applications. In this paper, we consider the cell-free (CF) massive MIMO framework with implementing MEC functionalities. We consider multiple types of users with different average time requirements for computing/processing the tasks, and consider access points (APs) with MEC servers and a central server (CS) with the cloud computing capability. After deriving successful communication and computing probabilities using stochastic geometry and queueing theory, we present the successful edge computing probability (SECP) for a target computation latency. Through numerical results, we also analyze the impact of the AP coverage and the offloading probability to the CS on the SECP. It is observed that the optimal probability of offloading to the CS in terms of the SECP decreases with the AP coverage. Finally, we numerically characterize the minimum required energy consumption for guaranteeing a desired level of SECP. It is observed that for any desired level of SECP, it is more energy efficient to have larger number of APs as compared to having more number of antennas at each AP with smaller AP density.