Why isn't there an article before conflict in the following sentence?
Difference in the pronouncement leads to conflict.
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It's referring to the general concept of conflict, rather than the specific one.
You could say "leads to a conflict" or similar, but in doing so you're making a more specific statement about what sort of conflict it leads to. Maybe it's a petty conflict, maybe it's a major one. Maybe it's several years of conflict (see again no article there).
Leaving the article out allows you to be more circumspect.
"conflict" can be countable or uncountable. Countable and Uncountable Nouns
The biggest conflict of the 20th century was World War II. (countable)
Conflict between countries can escalate into war. (uncountable)
In your rather cryptic sentence we can demonstrate the difference.
Difference in the pronouncement leads to conflict. (uncountable)
Difference in the pronouncement leads to many conflicts. (countable)