What is the relation between pot odds and probability here?

Hi

I'm having a conceptual problem here I was hoping one of you sharp guys can help me with. I understand the relationship between odds and probability, that they are 2 ways of saying the same thing. For example if the odds are 4 to 1 I know the probability can be got by adding them for the denominator and the 1 is the num so 1/5 chance of success.

My problem is when I use this same logic for pot odds. Let's say there is $40 in the pot and $10 to call. I believe this is correct to say 40:10, or 4 to 1 pot odds. I'm having a problem however because this doesn't seem analagous to the prior example as I'm uncomfortable making a fraction out of this 1/5 or a percentage 20%. I think my problem is that this is no longer a probability problem because it's just a ratio between two numbers, I'm not trying to determine the chance of an event occurring. Yet I'm still using probability notation. I want to figure this out without comparing the pot odds to the odds of making my hand, I want to use the pot odds alone to come up with the theoretic breaking-even point, if I can.

Then, saying the pot odds are 4:1 as above, how do I use this information to determine my break-even percentage of how often I must make hand or win the pot to break even. I know it's 1/5 but, again not sure how they get this.

Please help me clear up my conceptual problems. Thanks.