What happens to the pressure of gas when only one molecule of it is placed in a very large container?
I think you have forgotten what pressure represents in terms of the kinetic theory of gases. When studying gas kinetics, you start by understanding the behavior of a single molecule/atom moving around a container and colliding with the surface and bouncing in random directions. Then you add a few more molecules/atoms so that now there are collisions and as long as the mean free path of the gas is less than the dimensions of your vessel you still have motion that acts in random diffusion-like behavior. Once sufficiently many atoms have been added that a given amount of area experiences a regular number of collisions per unit of time, then you have something that can be given as an average rather than a count of collisions. This is what pressure represents, an average force on a surface per unit area of molecular collisions on that surface. The instantaneous force can change for a given spot nanosecond to nanosecond, but averaging all spots over a span of microseconds will give an average force per area can be resolved which we call pressure.
The problem here that gives you a misunderstanding is that you have taken a behavior of an aggregation of many molecules and tried to apply it to a single molecule. This approach will disappoint. But to summarize and actually answer the question, pressure cannot describe a system of only one gas molecule, and is therefore undefined.