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For most items the chance of an attribute is specified: Sky Splitter:

15–20% chance to Smite enemies for 600-750% weapon damage as Lightning when you hit them.

But for some items it is not specified: Thunderfury:

Chance on hit to blast your enemy with Lightning, dealing 279–372% weapon damage as Lightning and then jumping to additional nearby enemies. Each enemy hit has their attack speed and movement speed reduced by 30% for 3 seconds. Jumps up to 5 targets.

Which chance does an item have, if the chance is not specified?

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There is no universal chance for such things to trigger (like the 20% for the area damage, for example).

Each item has its own triggering chance and afaik there is no way to see ingame how high this chance is. So the only way to find out how often an ability triggers, is to test it.

Thankfully, someone already did.

Lightning element. [Thunderfury, Blessed Blade of the Windseeker]'s proc has a 60% base chance that is affected by proc coefficient. [Thunderfury, Blessed Blade of the Windseeker] also has an internal cooldown of 1/attacks per second. Does not proc Paralysis.

I can't speak for its correctness and completeness, but it should serve as a good starting point.

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