Pathfinder's Master Alchemist and Elemental Equalibrium

In order to inflict Shock or Freeze you must pass two tests. For Ignite you only need to pass the first test.

1. Chance test. You must successfully roll Chance to Shock, Freeze, or Ignite. Note that Critical Strikes always have 100% Chance to Shock, Freeze, and Ignite, but are rolled per Skill Use, while actual stated stats of x% Chance to Y roll per Hit.
2. Minimum duration test. For Shock and Freeze, status ailment duration is based on the ratio of your Damage in one Hit vs the maximum Life of the target (by default). Ignite just has 4 seconds base duration. Every 1% of target max Life grants 60 milliseconds (ms) base duration. You need 300 ms to inflict Shock or Freeze (or Chill, which skips the first test) (default 5% with no duration bonuses)

Note that by default, the Type of Damage must match to contribute to the Duration. That is, only Lightning Damage contributes to Shock Duration and only Cold Damage to Freeze (and Chill). This can be modified by things like The Three Dragons unique helmet or that one Elementalist ascendancy passive that grants Elemental Conflux.

I mean, technically you could pass the 20% chance roll for Shock and Ignite on your Hit. But, 0 damage means 0 second duration and 0 Ignite damage. An enemy doesn't Ignite unless it takes a nonzero amount of Damage.