# naive bayes classifier with Exponentially distributed likelihood with big parameter

Just for the practice of it, I'm trying to do a naive Bayes classifier for data which has exponential distribution for the likelihood function, i.e. $$X_k=x|Y=1 \in Exp(\lambda_k)$$ where $$k = 1,..., p$$ and p is the number of predictor\independent variables.

Now I'm facing an issue of my predictor variables being exponentially distributed with really big lambdas which I got from an MLE of the parameters with $$\hat{\lambda_k} = \bar{x_k}^{-1}$$. One of them is as big as 1451000. This gives me a lot of really small numbers of the predictors and when I calculate the product of $$P(X_k=x|Y=c)$$ I always get 0.

This is my dataset, it's basically a spam classification algorithm.

How can I tackle this issue, is this what is called the zero frequency problem? I read something about Laplace smoothing, but couldn't find how I can incorporate it in my scenario.