(dead body in kebab shop)
Wait, you don't know what kebab is made from?
Seriously though, this:
It's weird that eating something that was exposed to cigarette smoke actually gives you smokers breath.
Isn't as weird as it seems, actually. Taste is a quite limited sense (there are only 5 known taste sensations, a 6th probably exists, but is still disputed), and olfactory sense plays a big role in the overall impression that your brain gets as "taste".
It's entirely conceivable that you think you have smoker's breath because you have a remainder of the taste in your mouth (which is picked up by the olfactory system). And since you have only one sense of smell, you have no way of knowing the difference!