Is it distributed between the cards or the groups of them? Or, in other words, if I add more epic cards to my deck, do I get a better chance of hitting an epic card?

The probability of getting an epic card would be the same, but by adding more different epic cards the probability of getting a specific one gets smaller.

A random number is drawn between 1-100
if that number happens to be 1-5 the game draws you an epic, if no epic card is drawn the game will randomly add 1-3 points to the 'Uncommon drawing'
once a player has 15 of those points an uncommon card is drawn and the points are reset to zero.

This means it takes 5-15 common card draws to get single uncommon and 5% chance to draw epic card.

Uncommon cards are typically cards I don't want to be able to be spammed and epic cards reduce spam with their higher vespene costs.

Thanks.
That proably means I should remove some of the epic cards from my deck <sniff>