# Handling underflow in a Gaussian Naive Bayes classifier

I am implementing a Gaussian Naive Bayes classifier (so each feature is continuous and assumed to be coming from a Gaussian distribution). When evaluating the probability of a feature value in the test set, if the value is sufficiently far away from the mean (e.g. the mean and s.d. on the training data is say 0 and 1 but the test value is 10^10) then there is underflow. This is an issue because then the probability will be calculated as 0.0 so the log probability is undefined. Is there a standard way of handling underflow in this case?