Chord Progression I IV V

What on earth is IIIb? You're using an odd mix of methods to write out the progression, so it's not clear what you mean.

I'm going to hazard a guess though... In C you would have Cm Ab Bb Ab Eb F G? If that's correct, it would best be written as i bVI bVII V bVI bIII IV V. Even thought the b6 major chord is a diatonic chord, and VI can generally be assumed to mean b6 major, it's not guaranteed. With that in mind, it's not hard to indicate the specific scale degree a chord is to be built off of. It's not the "traditional" way, but that method is severely outdated and doesn't work well with a lot modern music.

Anyways, I'm sure there's a song out there that uses that progression, but why worry about that? You can't copyright a chord progression. Besides, there's an infinite number of ways you could arrange any progression. If it comes out sounding too much like some other song, that's your fault for not coming up with an original arrangement.

A chord progression is just some chords and the order in which they are played.

Try this: G, C, D. That's the most common type of progression, referred to as the i-iv-v progression. Starting with the key (in this case - G) as the "i" chord, the "iv" and "v" chords are the 4th and 5th chords you would play if you went straight down the scale.

You can see this in everything from blues, to punk, to pop etc.

Here's another progression, taken from Metallica's "Fade To Black".

Am, C, G, Em.