I can easily compute how likely it is that one of the Elizabethan authors was the greatest author of all time given that hypothesis 2 is false:

...Yes, the answer is 0, since hypothesis 2 is "an Elizabethan author was the greatest author of all time":

Hypothesis #2 is that something about the time that Shakespeare wrote in made it very likely that we would elevate some writer from that time period to "Greatest Writer Ever".

(I think you should reword this to clarify what you really meant, whatever that might be.)