1/381924
Calculation: When you use /nms maxgen8 command for seeing the total no. of moves, it shows 844 moves. Counting unselectable moves from Metronome it's 63 (source), along with 18 from Z-moves for each type, and another 19 from Max moves from each type, signature z-moves: 17, G-Max moves: 34 and moves deleted from Gen 8: 75. These moves can't be selected from Metronome. Total no.: 226. Now: 844-226=618, so 618 moves can be chosen randomly from metronome, or 1/618 is the chance of a move from Metronome. Chance of getting it twice would be 1/618 square, = 1/381924
Hope this helps!