We can show this contribution in another way. For each feature, you need to compare the commonness (probability) of that feature (f) independently against its probability under the given condition. ( P(f) vs. P(f | x) . For example, if we know that the probability of being a man is 90% in a society and 90% of smokers are also men, then knowing that someone is a man doesn't change anything (10% * (90% / 90%) = 10%) . But if men contribute to 40% of the society, but 90% of the smokers, then being a man increases the chance of being an smoker (10% * (90% / 40%) = % ) . In the same way, if the probability of being a man was 95% in a population, then regardless of the fact that the percentage of men among smokers is high (90%)!, the evidence of being a man decreases the chance of being an smoker! (10% * (90% / 95%) = %) .