# Bayes theorem for dependent events

I am new to Bayes theorem; In Naive Bayes, we assume that events are independent. How does Bayes theorem modify if the events are dependent ?

The theorem stays the same. The term Naive Bayes is short name for Naive Bayes classifier. Here, while calculating the posterior probability, we assume conditional independence over the input dimensions: $$p(\mathbf x |C_k)=\prod p(x_i|C_k)$$
So, we have the class posterior as below: $$p(C_k|\mathbf x)=\underbrace{\frac{p(\mathbf x|C_k)p(C_k)}{p(\mathbf x)}}_{\text{Bayes Classifier}}=\underbrace{\frac{p(C_k)\prod p(x_i|C_k)}{p(\mathbf x)}}_{\text{Naive Bayes Classifier}}$$
Without the naive assumption, Bayes classifier directly calculates the class conditional probability, $$p(\mathbf x| C_k)$$. So, the theorem has nothing to do with the naive assumption we make. See here for more on terminology.