Can I determine the Kullback-Leibler distance $ D_{\mathrm{KL}}(P\parallel Q)=\sum_{i}\ln\left(\frac{P(i)}{Q(i)}\right) P(i) $ between the following probability distributions?
P(X) = 1 2 3 4 5 6 7 8 Q(X) = 1 2 3 4 5 6 7 8 2/8 1/8 1/8 0 1/8 2/8 0 1/8 0 1/8 1/8 2/8 1/8 0 2/8 1/8
These are 2 different probability distributions and sometimes in the sum $\ln(P(i)/Q(i)) = \infty$ and $P(i)=0$. Because somethimes the $P(i)$ or $Q(i)$ is $0$. How I can handle it?