This technical note focuses on efficiently identifying the unknown or time-varying randomlatency probability (RLP) of the measurements in the networked multi-sensor system by resorting to expectation maximization (EM) framework. Firstly, a novel scheme is proposed for equivalently decomposing the complete data log-likelihood function into a summation form parameterized by RLP. Secondly, the rapid computation of the expectation in E-step is achieved by skillfully introducing Jessen's inequality to avoid the state augmentation of the traditional method. Thirdly, the analytical identification result of RLP is obtained in M-step by constructing Lagrange operator to maximize the expectation with the parameter constraint. Naturally, such analytical result is so simple that it can be quickly carried out, which is demonstrated by quantitative computation complexity analysis. Finally, an example motivated by the maneuvering target tracking application is presented to show the superiority of the new method.