I don't think you logic works. Your table says that if a 0 is in-putted then there is a .1 chance of getting a 0 and a .8 chance of getting a 1. That leaves a probability of .1 or something else happening, but it you add a third state it is no longer a not gate.

In other words, a not gate, regardless of the implementation must have it's columns sum to 1. This is a fundamental principle of probability and the definition of a not gate.