The NLTK Naive Bayes is of the Multinomial variety (typical with classification), the clue to this is that the Gaussian Naive Bayes is typically used on data that is continuous (not typical of text classification).
The official documentation for the NLTK Naive Bayes can be found here: https://www.nltk.org/_modules/nltk/classify/naivebayes.html
Key text sample-
A classifier based on the Naive Bayes algorithm. In order to find the
probability for a label, this algorithm first uses the Bayes rule to
express P(label|features) in terms of P(label) and P(features|label):
| P(label) * P(features|label)
| P(label|features) = ------------------------------
| P(features)
The algorithm then makes the 'naive' assumption that all features are
independent, given the label:
| P(label) * P(f1|label) * ... * P(fn|label)
| P(label|features) = --------------------------------------------
| P(features)
Rather than computing P(features) explicitly, the algorithm just
calculates the numerator for each label, and normalizes them so they
sum to one:
| P(label) * P(f1|label) * ... * P(fn|label)
| P(label|features) = --------------------------------------------
| SUM[l]( P(l) * P(f1|l) * ... * P(fn|l) )