In this setup, we're assuming that it's Oranguru and Maushold (holding King's Rock) vs Oranguru and our target Pokémon. The target is frozen, confused, and infatuated with the opposing Oranguru (since Maushold cannot learn Attract). Maushold uses Population Bomb on the target and lands all 10 hits, then both the ally and opposing Oranguru use Instruct on Maushold, and both of the following Population Bombs also land all 10 hits. Assuming all the above happens (we will not be considering the odds of these Pop Bombs all landing), the target Pokémon then moves last, and we want to know the odds of it successfully landing a hit.
In Champions, a Pokémon that is frozen has a 1/4 chance of thawing on each of the first two turns, and a 100% chance of thawing on turn 3. We'll assume that the Pokémon has been frozen for less than 2 turns.
Pokémon that are confused have a 1/3 chance of hitting itself, and a 2/3 chance of moving normally.
Pokémon that are infatuated have a 50% chance of moving or being immobilized.
Each hit of Population Bomb has a 10% flinch chance, and we've landed it 30 times. The chance of it not flinching 30 times in a row is (9/10)^30, which is a 4.23911583% chance, or about 1 / 23.6.
Now we just multiply the odds of moving at each stage together:
1/4 * 2/3 * 1/2 * 1/23.5898249 = 0.353259652%, or about 1 / 283
