>>9537935So? I have no problem with P(A|B) > P(A)
If something exists there is more likely to be evidence for it.
>>9538389My problem with the OP is defining the complement of A as absence of evidence.
In a way it is, but it's such weak evidence that's pretty much insignificant. Let's take the case of elephants in my room and use Def 1 from OP (P(B|A)>P(B|-A))
We have from Bayes rule:
P(B|-A)=P(-A|B)P(B)/P(-A)
P(-A) is pretty much one, since I can confirm there is no elephant in my room. However, P(-A|B) is nearly zero, since why would and how would an elephant get to my room even if it did exist? For most cases you're pretty much just saying that P(B|A)>0, which tells you nothing.
The probability that an elephant is in my room is greater if they exist, but it's like saying the very low probability that they'd be in my room in the first place makes it so that inequality is always satisfied, giving you no information.