How to estimate probabilities of different classes for a Text
If I understand correctly, we are interested in soft multilabel classification, where a single text can have multiple correct genres.

According to your comment, we don't have any training data, just a list of keywords associated with each genre.

We can try computing the similarity between each document and each keyword list:


Normalize the document (convert to lowercase, remove punctuation, diacritics, non-alphanums, etc)
Remove stopwords
Convert the document to tf-idf vector over our genre keyword vocabulary: Each document gets an n-length vector where each entry is the frequency of the ith genre keyword in the document. Normalize this vector to magnitude 1.
Convert each genre keyword list to a tf-idf vector in the same way (again over the keyword vocabulary for all genres).
Compute the cosine similarity between the document vector and each genre vector.


For each document, this will give us a number in the range [0,1] for each genre. For example:

         Comedy Drama Fiction Romance Mythology Adventure
Text #1: 0.15   0.11  0.03    0.00    0.00      0.07


If we were doing single label classification we could normalize each row to add up to 1 and we might have a working model. However there is no such trick for multilabel classification here. We don't have a good way to calibrate these values into probability estimates.

At this point the only solution I see is to build a small training set so we can fit our model to actual data. 

After gathering some training examples, we can run a multilabel regression with sigmoid activation and binary crossentropy loss with the cosine similarities as input features to get a probability estimate for each class.

Using this method our list of genre keywords will at least save us having to build a large training set to solve the problem directly with bag-of-words or similar approaches.