EDIT 3: I retract the following paragraph because I now understand what Wes_W wrote.

I know, that's why I said "There are possible rational justifications". I mean your reasoning make sense mathematically. But why would your distribution be two deltas at 10^-4 and 10^-16 and not more continuous? It's not a rhetorical question, I want to know the answer -if there's one-, but I don't see how it could be that way. Do you think you are rationalizing your answer? (again, it's not a rhetorical question)

EDIT: After reading other comments, I think another way a discontinuity might be justify is like this: going faster than light speed is either possible or not.

A. if it is, then if there's a sufficiently advance civilisation (anywhere in the Observable Universe) it would probably be able to colonize most of the(ir) observable universe. (so the probability that there are aliens in the Milky Way is similar to the Observable Universe).

B. if it isn't, then it's the probability that there are aliens in the Milky Way is a lot lower than in the Observable Universe.

EDIT 2: Can you think of other reasons for the discontinuity? With what probability do you think the speed of light is the maximum speed one can transfer information/energy?