I personally was thinking about whites vs. non whites.

White men vs. non-(white men) is what you are analyzing. We have to be careful here because there are implicitly two coupled variables.

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Bamboo was analyzing (White vs. non-white) men. Thus, in a way he limited the "universe of discourse" to men. Considering that 99% of the shooters were men, this is in fact a reasonable approximation.

Bayes rule can be used here for inference:

The probability of being a white male given that the person is a shooter is 0.7.

The probability of being a male given that the person is a shooter is 0.99.

The probability of being a white male shooter given that he is a male shooter is then 0.7/0.99 which i still about 0.7.

The probability of being a white male given that the person lives in the U.S. is about 0.32.

The probability of being a male given that the person lives in the U.S. is about 0.50.

The probability of being a white male given that he is a male in the U.S. is about 0.32/0.50=0.64.

So the numbers work out to be pretty much the same whether we are considering race in the general population or race among men. We are assuming that race and gender don't correlate. But that seems like a reasonable assumption.