Legendary Fish are Fish of the highest Rarity, which is "EXTREME" in Fishing. They arent calculated with certain formulas like the others (that go up to like a chance of 1/500), no, these have special chances.
These Fish are almost never seen and very hard to catch.
Only 1 is currently known: The 'Giant Octopus'. Its rarity to see is 1/7500 and to catch it you have to react in under 0.4 seconds. To compare: normal reaction time of a warned human is 0.5 seconds.