Pr(A, given B) has been defined as the ratio of Pr(A and B) to Pr(B), provided that Pr(B)>0. This suggests a psychological question, namely, whether estimates of Pr(A, given B) arise in the mind via such implicit calculation of Pr(A and B) /Pr(B).
So we did a simple study where we first presented people squares, circles, and triangles in red, blue, and green on a computer screen and then asked them to estimate conditional probability of a certain shape given a certain color (or a color given a shape).
What did we find? People were not following this ratio definition of Pr(A and B) /Pr(B) in their mind while doing conditional probability judgments. So what kind of computation were they using then? This awaits future exploration.
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