Using Autonomous Mobile Robots (AMRs) to collaboratively complete tasks has received a lot of attention in recent years from both industry and acedemia, especially in applications related to manufacturing automation. However, in spite of the technological progress, there are many challenges yet to be addressed in prioritized task allocation and scheduling of a school of AMRs in real time. This paper focuses on the real-time task allocation problem for a school of AMRs, i.e., given a prioritized task list and multiple AMRs, determining the set of tasks to be completed by each AMR. This paper proposes a probabilistic task allocation method which formulates the problem as a log-likelihood maximization problem, and uses a cyclic optimization scheme. This algorithm is shown to perform better when compared to commonly-used algorithms for asymmetric clustering. This proposed algorithm can be combined with scheduling methods to generate a ‘cluster-first, order-second’ solution to the multi-AMR task planning problem.