How likely is it to contract oral herpes by sharing a cigarette?

Herpes and cigarette. It is possible if you have a break in the mucosa or skin barrier and the other person happen to have placed the cigarette directly on an open lesion. But very unlikely - but still possible and it should be avoided.
Rare but possible. If the person you are sharing with is currently experiencing an outbreak then virus particles on the cigarette can get through a minute tear in you lip and infect you.
Possible. If the person has an active lesion, then there is a chance for passing the virus along.

Related Questions

Is it possible to contract oral herpes from sharing a cigarette?

Definitely. If the other person sharing has an active lesion around the mouth it is quite possible. Read more...
Yes. Yes... If the oral herpes vesicle is present, it is extremely contagous. Drinking from the same glass, kissing or smoking the same cigarette are all possible ways of contracting oral herpes. Read more...