In this context, putting error bars on a probability doesn't really make sense. Your uncertainty about the probability is already encapsulated in the probabilit

In this context, putting error bars on a probability doesn't really make sense. Your uncertainty about the probability is already encapsulated in the probability itself. In other words, 'more uncertain than 5%' wouldn't be 5±x% , it's be, say, 6%. If you have no information at all -- you're as uncertain as you could possibly be -- the probability would just be your prior for this event, and the more data you get pointing to the event either happening or not, the more the probability will move away from your prior towards either 0% or 100%.