To be clear: this precise situation, where everyone has an exactly equal chance, will happen only on checks where the DC is exactly equal to 20 + the highest modifier in the party on that particular check.The "new" nat 20 rule essentially gives everyone an equal chance to succeed regardless of their skills or proficiencies.
Part of the discrepancy between my position and others' is that it seems this is very rare in most games, but fairly commonly in my games.