I don’t know if I would believe them. To put it bluntly a fairly large number of people lie. If you never lied and explained that you had a conviction but you were innocent, I’d be significantly more inclined to believe you.

I also don’t know that I would care. Someone that got popped for smoking dope as a teen in the 90s is not a crime I’m worried about. Innocent or not doesn’t matter. Something more violent or problematic to the company is going to be a different story.

If you were honest from the start I’ll give you time to explain, but if you lied on the resume, that gets to the “problematic for the company” bit.