TLDR: Usually you start with num_interesting_event / total_measurements

This biases the result toward 0 or 1. Instead, you can bias toward .5 if you know that both sides of a binary outcome are possible: ( num_interesting_event + 1 ) / ( total_measurements + 2)

At 0 measurements, your probability is .5 based on the rule of succession instead of 0, 1, or undefined. Further measurements effectively iterate on this initial fair guess.