Pokemon Go players who get the chance to battle Mewtwo should feel pretty confident about their chances. Game developers recently updated the GAME_MASTER file for Pokemon Go and edited Mewtwo's base capture rate to 6%.
The base capture rate is the baseline for a player's chances of capturing Mewtwo before other catch bonuses are factored in. Basically, if a player hit Mewtwo with a Premier Ball without any accuracy bonuses, berry bonuses, or other bonuses factored in, they'd have a 6% chance of capturing it per throw.
Of course, the capture rate goes up significantly when other bonuses are included. For instance, a player who hits Mewtwo with a "Great" Curveball, has a Gold Medal for capturing Psychic-Type Pokemon, and fed Mewtwo a Golden Razz Berry has a 38% chance of capturing Mewtwo per throw. If a player can replicate that throw consecutive times, they should be able to capture Mewtwo within three throws.
Those are pretty good odds, especially compared to other Legendary Pokemon in the game. For comparison's sake, Mewtwo's base capture rate is twice as high as the Legendary Birds and three times higher than the Legendary Beasts currently running around in the game. Mewtwo even has a higher capture rate than Pokemon like Tyranitar, Venusaur, and Charizard, all of which are currently Level 4 Raid Bosses.
Pokemon Go likely boosted Mewtwo's capture rate based on its relative in-game rarity. While other Legendary Pokemon will randomly appear at gyms, Mewtwo will only be available in special EX Raids. Players have to be invited to EX Raids, and there's no real indication as to how common they'll be for players. It's possible that cities could only see one Mewtwo raid per day or even less.
Mewtwo raids are beginning today, although Pokemon Go is staggering its rollout to allow more time for balance testing and beta feedback. We'll have more coverage of the upcoming Mewtwo raids, so stay tuned.