Any festival which has 6.1% legendary hatch rate. @Killerdog has figured out the exact numbers. Remember that a “Special egg” has 4% rate.
Entirely based on luck. You might get a legend or you might not. If you get a legend you might get a featured or you might not. There’s pretty much nothing we can do to influence that. As far as probability goes. With 6.1% hatch rate you “should” hatch one legendary every 2 packs, because according to the rates 0.061x20 = 1.22. Of course this starts applying better only after you’ve made thousands of hatches.
Also, you can check the hatch rates now from the “Info” tab on the egg.
Just clarifying in case there’s any confusion (Floccuboi’s maths in the first reply is a bit dodgy and might have mislead).
Talking about festivals: the chance of mythic is 1%, legendary is 6.1%, etc.
The whole “10x/20x/30x chance of getting a featured” is unrelated to that. All that’s doing is making, say, a legendary hatch more likely to be one of those compared to the standard pool.
The exact chance of a featured changes from egg to egg…
There are 10 mythics in the standard pool. When 1 is featured and is 20x chance that effectively increases the pool size to 30, with 20 of them 30 being the featured mythic. So 20x chance = 2/3 of a mythic being the featured and 30x chance = 3/4.
There are 43 legendaries in the standard pool. In most eggs there are 4 featured with 10x chance. Hence the pool size is effectively 83, with 40/43 being featured legendaries. So in most eggs it’s roughly 50% chance of legendary hatches being a featured monster. When there are 3 featured the pool size is 73, with 30/73 being featured. That’s roughly 40% chance of a legendary being a featured. If they ever feature something like 6 legendaries (like last anniversary) then it’s 60/103, roughly 60% chance of a legendary being a featured.
Since most eggs right now feature 4 legendaries and with 10x chance I like to think of it as requiring 2 legendary hatches in order to get a featured. Outside a festival that’s 5 packs, in a festival that’s 3-4 packs. If you’re looking at an egg and thinking you’d really like 2/4 of the featured legendaries then double that number (10 in special egg, 7 in festival egg) and that’s probably what you need to spend to get one of those two.