During the water event back in March magikarp were very common, but I caught < 100; of those, 3 were shiny. I was very lucky and have evolved them all (despite mediocre IV''s, but who cares - I like to show them off in gyms).
I think the odds were 1:256 during the event (per Silph Rd), but have to be much rarer now. I thought I'd never find another one (total seen 961/caught 918), but just a few days ago my 4th shinykarp appeared (and has since evolved).
A combination of RNG, location and luck!
I know many players still don't have one and a few have several. Good luck for catching one soon! They're fun to have.