They all basically mean to forbid or stop something from happening. Prohibit is when someone (or something) else or an outside force is forbidding something. For example: the government prohibits the use of drugs. Inhibit is from within oneself or an internal force that is preventing something. This is usually when psychological, mental or spiritual forces are doing the forbidding. For example: my desire to be healthy inhibited me from taking drugs. Prevent is the general verb to stop something from happening. For example: I am prevented from taking drugs. Prevent is not explicit, and doesn't tell you if the prevention was via a prohibition, inhibition or other means.

That's an excellent question! "Inhibit", "prevent", and "prohibit" are all used in similar contexts but have very distinct meanings. "Inhibit" means to slow down or stop the process of something, "prevent" means to keep something from happening altogether, and "prohibit" means to strictly disallow something from happening, regardless of if it is successful or not (the law prohibits illegal things, but they still happen anyway), and implies punishment for engaging in said thing.