# PDFs and probability in naive Bayes classification

I have seen a few times the technique of using the Gaussian PDF for continuous features in Naive Bayes. here and here. Illustrated in the first link:

How is this possible? I always learnt that the PDF is not a probability -- as the probability of any exact value of x is zero.

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 See this for more details regarding my answer, and this for (I think) more details regarding @procrastinator's. – Neil G Apr 19 '12 at 3:56

$$L(c \mid x=v)=\frac{1}{\sqrt{2\pi\sigma_c^2}}e^{-\frac{(v-\mu_c)^2}{2\sigma_c^2}}$$
$$P(c=c' \mid x=v) = \frac{L(c=c' \mid x=v)}{\sum_{c_i} L(c=c_i \mid x=v)}.$$