Of the 34 vintage skins, the most common, Bewitching Nidalee, appears once every 971 games in North America. The least common, Ice Toboggan Corki, appears once every 116,586 games in North America. "We think it's important to solve this, especially since we believe skins are primarily about self-expression and fun, not exclusivity," the company stated in its announcement.
Players who already own the skins will be compensated in several ways: they'll receive a number of Riot Points equal to the amount they originally paid for the skin, a special visual effect on their champion's image during match loading, and an exclusive summoner icon.
To see all the skins which will be re-entering the Fields of Justice, check out the official post. If you have any questions you want to ask Riot regarding the skins, they'll be holding an AMA on Reddit October 15, starting at noon, Pacific.