Basically my question is that when a material (let's say air to be specific) undergoes dielectric breakdown with enough voltage, how conductive does it becoming during the breakdown? Maybe that depends on different factors, so let's just say for air in standard conditions and with just about enough voltage for it to breakdown (around 30 KV/cm). I saw a question asking about this which didn't have any answers.
If you download this thesis pdf, at page 22 you will see the resistance curve of a typical arc (5kV, 30kA), it's (>0.5Ω)→0.15Ω according to the paper. I believe the gas is air. Found it on google, 3rd link.
Here's the figure I'm referring to:
Later at around page 52 there's a couple of more similar graphs for different pressures. But the figure above matches the air figure at page 53.