I am saying that X is evidence for Y vs Z if and only if observation of X increases the probability of Y relative to the probability of Z. If you can think of a context in which that is unreasonable, then please state the context in unambiguous terms and explain clearly why you think it is unreasonable.
Several contexts:
1) X, Y and Z may be ill defined.
2) The word "observation" is ambiguous in some contexts. Specifically, we do not generally accept observations using methodologies like remote viewing, dream states, or from untrusted proxies.
3) In some contexts a mathematical increase in probability cannot be translated into frequentist terms, such as with binary outcomes. So, for example, there is no meaning or testable difference between the statements: Hilary has a 60% chance of winning the election tomorrow and Hilary has a 65% chance of winning the election tomorrow. (See next for subjective version instead of frequentist.)
4) In cases of belief (the closest to this thread), there is no value/meaning in saying I believe Y 20% but this new evidence makes me believe Y 25%. In many contexts we believe something or we do not in a binary manner.
5) The evidential value of an observation of X (increase or decrease probability) may be dependent on other observations. Since you wanted clear examples, I'll construct one:
a) The murder was committed with a gun (given)
b) The suspect has a gun (observation X)
c) The observation X has evidential value because it increases the probability of Y (he did it) over Z (he didn't do it).
d) The suspect is paralyzed from the neck down (observation W)
What happens to the evidential value of X? The fact that the suspect had a gun is suddenly no longer evidence at all, since the suspect is incapable of using a gun. We still observe X, but W has changed the meaning of X and X is no longer evidence of our proposition. W now has evidential value and influences our probabilities, but then along comes V, and so on.
The point is that X satisfies the conditions but in the real world, X comes with baggage, context. And the important thing is that we, the experimenters, often choose or limit the context.