Yes they will. It just cannot proc 3 times on one enemy. It's to help AOE. However, AD procs on skill cast. So if AD procs and knifes hit 3 targets. At 100% AD it should hit all 3 targets for 9*40,000 and all enemy's in AD range for 3*40,000. So it's an absolutely massive buff overall.
This item literally triples the damage of the set if there's more than 3 enemies grouped and you have decent AD.