The obvious answer to the murder quote is that you look harder for evidence around the crimescene, and go where the evidence leads, and there only. The more realistic answer is that you look for recent similar murders, for people who had a grudge against the dead person, for criminals known to commit murder in that city... and use those to progress the investigation because those are useful places to start.

I'm wondering what pjeby has realised, which turns this naive yet straightforward understanding into wrongthought worth commenting on.

That isn't a wrongthought. Factors like you mention here are all good reason to assign credence to a hypothesis.

If evidence is not facts which reveal some result-options to be more likely true and others less likely true, then what is it?

Yes, no, maybe... that is exactly what it is! An example of an error would be having some preferred opinion and then finding all the evidence that supports that particular opinion. Or, say, encountering a piece of of evidence and noticing that it supports your favourite position but neglecting that it supports positions X, Y and Z just as well.