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Anyways, simply put the Legendary Birds spawn in their own respective Biomes which in this case are, Ice Mountains for Articuno, Extreme Hills for Moltres, and Forest Hills for Zapdos.
As far as rarity goes, Zapdos is the most rare of the Trio, with Articuno being the least rare, and Moltres not too far ahead of Articuno.
As Explained in the Video, you can see that based on the spawn rates of other pokemon in the biome, they all have an equal spawn influencer, it's just a matter of how many other Pokemon can spawn in that area as well. Forests happen to be crawling with all sorts of wildlife, making Zapdos that much more rare. All of the birds have a Spawn Influencer of 1, as well as the other Legendaries added into the game at the moment.
Keeping this in mind, all you have to do is add the spawn rates of all the Pokemon in the biome together, and it will spawn once out of that many spawns. For example, Articuno has a spawn rate of 1/526, Moltres has a spawn rate of 1/571, and Zapdos has a spawn rate of 1/1491 for the reasons explained above.
I hope you found this helpful!