PoE2 uses an ailment-threshold model rather than a flat per-hit chance. Each target has an ailment threshold roughly equal to half of its maximum life, and the size of your hit relative to that threshold determines how much you build toward an ailment.
Non-damaging ailments (Shock, Freeze, Chill, Electrocute, Heavy Stun, Pin) and damaging ailments (Ignite, Poison, Bleed) scale differently. Larger hits relative to the target build ailments faster, which is why bosses with very high thresholds are harder to freeze or shock.
Critical strikes and high single-hit damage make ailment application far more reliable than spreading the same damage across many small hits.
Ignite deals fire damage over time and is built up through the Flammability debuff: roughly each 5% of a target's ailment threshold dealt as fire adds about 1% chance to ignite, and at 100% Flammability all fire hits ignite. This replaces the old flat per-hit ignite chance.
Poison stacks as chaos damage over time. Its base damage is commonly cited as around 20% of the combined physical and chaos damage of the hit per second (this exact coefficient is single-source and should be treated as approximate).
Bleed deals physical damage over time and remains a static chance-based ailment rather than a threshold-scaled one.
Shock increases the damage the target takes. Build-up is threshold-scaled (around 1% chance per 4% of the ailment threshold dealt as lightning).
Freeze locks a target in place; Chill slows it. Both scale with cold relative to the target's threshold.
Electrocute, Heavy Stun and Pin are additional build-up ailments. Their exact coefficients are not fully confirmed across sources, so plan around the general 'bigger hits build faster' rule rather than precise numbers.