Conditional Information

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While trying to convert an equation involving probabilities into an equation involving information, should conditional probabilities be converted just as the notation suggests? For example, does $$\Pr(W_3\ | (C_1\ \cup\ C_2))$$ become $$.5^{I(W_3\ | (C_1\ \cup\ C_2))}$$ I can't find anything that says how to interpret this "conditional information," assuming it is indeed a real quantity. I have found mutual information, conditional mutual information, and conditional entropy, but I don't think those exactly fit here. Is this conversation correct, and if so, what is the meaning of this conditional information?