Antimicrobial peptides (AMPs) produced by multi-cellular organisms as their immune system's defence against microbes are actively considered as natural alternatives to conventional antibiotics. Although substantial progress has been achieved in studying the AMPs, the microscopic mechanisms of their functioning remain not well understood. Here, we develop a new theoretical framework to investigate how the AMPs are able to efficiently neutralize bacteria. In our minimal theoretical model, the most relevant processes, AMPs entering into and the following inhibition of the single bacterial cell, are described stochastically. Using complementary master equations approaches, all relevant features of bacteria clearance dynamics by AMPs, such as the probability of inhibition and the mean times before the clearance, are explicitly evaluated. It is found that both processes, entering and inhibition, are equally important for the efficient functioning of AMPs. Our theoretical method naturally explains a wide spectrum of efficiencies of existing AMPs and their heterogeneity at the single-cell level. Theoretical calculations are also consistent with existing single-cell measurements. Thus, the presented theoretical approach clarifies some microscopic aspects of the action of AMPs on bacteria.