In this presentation, we introduce a Bayesian updating method for inter-event times of different magnitude thresholds in marked point process, apply it to time-series of the ETAS model [1], and discuss the effectiveness in probabilistic forecasting of forthcoming large event considering the information on smaller events. To investigate magnitude threshold dependence of the inter-event time distribution of earthquakes, the conditional probability between inter-event times of different magnitude thresholds is proposed [2]. This gives the one-to-one statistical relationship between inter-event times of different magnitude thresholds. Firstly, we show the Bayesâ€™ theorem on this conditional probability and derive the representation of the inverse probability density function. Secondly, we extend it to the Bayesian updating that gives the relationship between multiple intervals for lower threshold and an interval for upper threshold. We show the derivation of the inverse probability density function and its approximation function for uncorrelated marked point process (background seismicity in the ETAS model). The condition for the inverse probability density function to have a peak is also shown. The approximation function consists of two parts, a kernel-part that determines its outline and a correction term. The former has an easy form to handle numerically and is applicable to the time-series with correlations among events. Thirdly, based on the results for uncorrelated time-series, we apply the Bayesian updating method to time-series of the ETAS model. The mode of the approximation function is numerically shown to be nearly the same as that of the kernel-part. Therefore, the mode of the kernel part is used as the estimate of the occurrence time of forthcoming large event. By using the relative error between the estimate and the actual occurrence time of large event, effectiveness of the estimation with the approximation function is statistically evaluated. As a result, it is shown that if the time-series is dominated by stationary part, immediately or long after the large event, the forecasting is effectively conducted. [1] Y. Ogata, Ann. Inst. Statist. Math. 50(2), 379 (1998). [2] H. Tanaka and Y. Aizawa, J. Phys. Soc. Jpn. 86, 024004 (2017).