the legendary pokemon you catch there is Azelf mostly.
this is the chances
Azelf: %10 of finding it
articuno: %0.001 IN SOME GAMES IT IS 0.00
(AFTER BEATING ALL GYM LEADERS)
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Go to Lake Verity which is in Twinleaf Town.
Lake Valor, Lake Acuity, and Lake Verity
You can get them. Piplup will be in Lake Verity, Turtwig will be in Lake Valor, and Chimchar will be in Stark Mountain. Or, you can choose them as your first Pokemon. Or, you can trade them with a buddy. this is actually wrong, those are the legendary lake trio in the lakes, the only way you can get all 3 is A) trade, B) Cheats to get them or C) get cheat to catch other people's Pokemon and find the trainers with them
In the water of Lake Verity
After you catch the main legendary (dialga, palkia, giratina) go to lake verity and mesprit will be in the cave in the middle of the lake. Talk to it and then it will flee and appear on your map app.