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I've been playing around in GeNie and I've been trying to construct a network of a certain structure, and I am not sure how to deal with impossible combinations of values for certain variables. Let's assume, we have three variables: A("the cat is under a table, the Sun is shining"), B("the cat is on a couch, it's cloudy"), C("it's raining, it's sunny) [see the picture].

And C is a common child for A and B. And when filling up a probability table, I was wondering how to exclude the possibility of "it's raining" (or it's sunny) given "the cat is under a table" and "the cat is on a table", as it can never be that if the cat is in one place, it can also be in another. Just physical impossibility. Any idea how to deal with it? Am I missing something fundamental here?

enter image description here

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First of all, you have constructed a poor example. The variables you have defined are not consistent: they have states from different sample spaces that are independent and may occur together at once (the cat is on the couch and it is raining).

If we assume that they are well defined, then A and B are dependent variables, so there should be an arrow between them. Then, in one of them you can exclude such probability by setting it to 0 in the conditional probability table. Then, the whole column in C does not matter.

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