articles rules tell that we should put an indefinite article in front of singular countable noun
i want a divorce
then why is here article not used in the following sentence
The idea of divorce, it should be the idea of a divorce or not
In "the idea of divorce", the word "divorce" denotes an uncountable noun. Concepts can be uncountable in the abstract, but actual instances of them can be countable in actual life. Examples: birth, death, marriage, divorce, marriage.