The catch rate for the three legendary birds is 3 in all of the games, including Platinum.
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You can capture Mewtwo in Cerulean Cave B1, Zapdos in the Power Plant, Articuno in Seafoam Islands B4, and Moltres at Mt. Ember Peak in FireRed.
You don't. Moltres, Zapdos and Articuno are not in this pokemon generation.
mewtow zapdos moltres articuno mew entei raikou suicune
You can catch Suicune, Entei, Raikou, Lugia, Ho-Oh, Celebi, and Mewtwo, Moltres, Zapdos, and Articuno.
Zapdos, Articuno, Moltres, Mewtwo, Entei/Raikou/Suicune (depends on what starter you chose).