Going into more details, 절대 (absolutely) is probably the closest of the three to "never".
(Note that 절대 is a rather colloquial version of the better sounding 절대로.)
- 그런 일은 절대(로) 안 일어나요 = That kind of things absolutely don't/won't happen = That kind of things never happen.
- 이건 절대(로) 만지면 안 돼요 = You should never touch this.
전혀 is "(not) at all' as was mentioned, which can mean "never" in certain contexts.
- 그런 일은 전혀 없어요 = That doesn't happen at all = That never happens.
못 is more subtle. It normally means "be unable (to do something)" but there is a usage (advanced kind) that can be translated as "will not" or "will never", i.e. a strong refusal to do something. This sounds confrontational, so it's not used in normal everyday situation.
- 무슨 말을 하셔도 그렇게는 못 해요 = No matter what you say, I won't/will never do that.
Also note that "never" referring to past experiences is not expressed using any of these words. You need a phrase like "-(은) 적이 없다" for that.
- 저는 (한 번도) 뱀을 가까이에서 본 적이 없어요 = I have never (even once) looked at a snake up close.
In short, there is no single phrase that corresponds exactly to "ever" or "never".