A reader has asked me to explain the exact procedure after the Host falls to the floor during Communion. There is not much written in the Roman Missal, but I do know what should be done.
This subject is addressed in the General Instruction of the Roman Missal, No. 280:
"If a host or any particle should fall, it is to be picked up reverently. If any of the Precious Blood is spilled, the area where the spill occurred should be washed with water, and this water should then be poured into the sacrarium in the sacristy."
I know that the fallen host should be consumed by either the priest or the communicant (whoever can get to it) as quick as possible. Afterwards the priest (or servers) should cover the spot of the fall with a purificator (preferably two and lay them over each other in the shape of a cross). Same goes with the spilling of the precious blood (only you can use a corporal to cover a larger area so that the blood isn't trampled on). Then the priest will clean the area removing all fragments and washing it with holy water.
I do not know about the priest prostrating himself to kiss the area in which the Body or Blood had fallen. Yet, it is a wonderful gesture!! As you said, "Those priests established a firm belief that Christ is truly present in the Blessed Sacrament!"
We should pray for priests to have such faith in the Blessed Sacrament as the ones you have described! It all comes back to whether or not we really believe that we are dealing with the True Body and Blood of our Savior Jesus Christ.