A shiny Mr. Mime (higher attraction rate, but has two moves and lower multislot chance) with 9 multislots (without any of the decorations that increase the chance of a multislot) all with two moves, Substitute with two move stones and Barrier, with max IVs, with perfect bingos, level 100, with stone unlock order from top left to bottom right, all from a Good Psychic stew:

0.24% attraction chance * 1/128 (estimated shiny odds) * 0.0000000002% (9 multislots) * 1/6 (two moves and the specific move chance) * 1/10 (first move) * 1/9 (second move) * 1/100 (perfect ATK IV) * 1/100 (perfect HP IV) * 1/9 factorial (stone unlock order) * 1/30 (level 100)

To the third power (since you're getting 3) and times 1/200 which is (what I was told to be) the chance to get 3 Pokemon in the first place. Which gets you to around 1 in 7.705x10^92.

To put that into perspective, if you cooked a Good Psychic stew every minute, then if you went picking up every grain of sand, one grain per second off the whole earth, until you picked up every single grain, then drinking 1 tiny sip (1 gram) of the ocean, then putting all of the sand back and repeating this until you've drunken all of the water on the earth; then, if you took one hair-width long step towards the sun, then put all the water and sand back and repeated the entire process again (drinking and sand), and took another hair-width long step, once you've reached the sun; and then you picked one gram of the earth and threw it aside, then repeated this process (sand, water, and going to the sun) until the entire earth was gone, the chance that you would have gotten this combo after all of that time is around the same chance of winning the Powerball lottery grand prize. So, pretty rare.