Which if I understand; would go like this on explaining UFOs:

Naive Approach:

P(ALIENS) = 50% p(~ALIENS) = 50%

Time elapses and I find some new evidence that looks like this:

P(Evidence | ALIENS) = 30% P(Evidence | ~ALIENS) = 90%

Which gives my hypothesis (Its Aliens) a posterior probability of 25% => (50% X 30%)/(50% X 30% + 50% X 90%).

I want it to be aliens so I say that they're conducting studies on us which juices P(Evidence | ALIENS && Studying Us) = 100%. But because I have no evidence to back that up, the odds are no better than 50/50; and I have to drop the prior of my new hypothesis (UFOs are Aliens who Study us) to 25% (50% X 50%). This nets out a new posterior probability of around 27%.

P(ALIENS AND They Study Us) = 25% p(~ALIENS) = 75%

P(Evidence | ALIENS & They Study Us) = 100% P(Evidence | ~ALIENS) = 90%

I'm new to Bayesian logic and am still shaky with it, so there could totally be glaring errors I'm overlooking, but as I understand it that's what I was trying to get across - Every new caveat you add to explain away a poor data fit shouldn't juice your odds.