That does not imply that fish are snakes. Nor does the presence of scaled fish invalidate the observation that having scales is a defining attribute of snakes (it's just not a sufficient attribute to define snakes).
Here's a toy example. Imagine three equally sized groups of animals: scaly snakes, scaly fish, and scaleless fish. (So all snakes have scales, but not all scaly animals are snakes.) That's three data points (1,1) (0,1) (0,0) with probability 1/3 each. The correlation between snake and scaly comes out as 1/2.
You can also see it geometrically. The only way correlation can be 1 is if all points lie on a straight line. But in this case it's a triangle.
I am noting that the logical argument does not hold in the provided definition. If “some” attributes hold in a definition, you are expanding the definitional set, not reducing it, and thus creating a low-res definition. That is why I said: ‘this is a poor definition.’
That's a strange definition of "correlation" that you're using.
https://www.morphmarket.com/morphpedia/corn-snakes/scaleless...