Koi often chase each other and nothing comes of it at 3" the smaller one is two small to fertilize the eggs of the female and you would have more than one chasing the big female it would get very agressive with some damage to the female .
It is also getting very late in the season for koi to mate and if they did spawn man would you know it as there would b an overpowering smell of ammonia plus each female koi can hold up to 50,000 eggs which would have blocked your filters.
Koi keepers normally seperate off any females that have developed eggs to a large QT tank, "our own is 550 gallons imperial l with its own bottom drain filter pump 15 watt UV-C and venturie".
You would also place into the QT tank spawning mats , then when the eggs are laid and the milt spread over them you would remove the two koi and allow the eggs to develope in the best possible of water conditions...
We see this from time to time , it may well be that the larger koi is either attracted to the larger koi passing half digested food or that koi may have a prolapsed vent due to an internal bacterial infection.
From your description of your koi my first course of action would be to cut down on thefood, feed only as much as they can eat in 5 minutes and also have the larger !0" out to have a look at the vent to see if it is prolapsed .
Because if this is the case your going to need to treat this koi with either an antibiotic injection or with medicated feed.
Dave
Dave