I've seen rates of supernova for the milky way as 1 per century. So that's 1 per 10^13 star-years.

With 10^22 stars in the observable universe distributed uniformly we would expect something like 10^9 stars to supernova this year.

But we have to consider the speed of light. So what we are really asking is something like what is the probability that light will arrive at Earth in some interval from a supernova.

I'd imagine this is some integral over spherical shells receding into the distant past where there is some function defined on the shell which tracks stellar density as well as supernova probability. Beyond my expertise to even attempt napkin math.