1/10 chance of 1 in prize, so 1/10 of 1/10 of 1/10... So 0.00001% chance. Or about 1 in a hundred thousand.
However, there are 100,000 possibilities in all, and a lot are unlikely and happen. Like a mr.mime, phantump, phantump, phantump, Shauna, and Shauna in my trevanant deck.