What are the rarest mons that you can catch? Is there a tier list?

[winged sinew]

I'm trying to figure out which mons are the rarest to find, not to catch. More specifically, what are the chances of getting those mons?

My friend didn't touch Pokemon Sleep for 5 months and when he comes back on the final day of the Entei week, he finds Kangaskhan on the same day. How lucky did he get??

[warm sail]

Legendaries

The chances are... indefinite. Here is how the game chooses: you get to roll your spawns, taking away power, and the last spawn takes up the rest of your power for the night.