The spreadsheet below calculates the conditional probability of an earthquake given the date of the last earthquake, a time window, and the assumed mean and standard deviation of recurrence times. A range of probabilities comes out of using three simple commonly used models:
1) Assuming that the recurrence of large earthquakes are described by a time-independent Poisson process, such that a future earthquake is equally likely immediately after the past one and much later. The probability that an earthquake will occur in the next t years is approximately t/T, where T is the assumed mean recurrence time. Because Poisson processes have no “memory,” this model assumes that a future earthquake is equally likely immediately after one occurs and much later.
2) Assuming time-dependent models in which a probability distribution describes the time between earthquakes. In such models the conditional probability of the next large earthquake, given that it has not yet happened, varies with time. The probability is small shortly after the past one, and then increases with time. The spreadsheet assumes the the recurrence times are described by either a Gaussian or lognormal distribution with a specified mean and standard deviation.
For an example of the effect of different models and parameters on the estimated probability of large earthquakes in the New Madrid seismic zone click here
Download introduction to earthquake probabilities (pdf) from Stein & Wysession, section 4.7.3
Is the coast toast? Exploring Cascadia earthquake probabilities, GSA Today 27, Nov. 2017, 6-7.