Use 'providential' when an event's timing seems perfect and unusually beneficial, as if by fate. Her providential win at the lottery came just when she needed money for college.
Pro Tip 2/3
Positive Outcome
It implies something good or fortunate happens, not something bad or unfortunate. The rain stopping right before our outdoor event was truly providential.
Pro Tip 3/3
Not Deliberate
Stress that the event seems unplanned by humans; use 'providential' for lucky accidents, not intentional acts. Finding the lost key in the trash on garbage day was providential.