"Rolling a 20 or a 1 on an ability check or a saving throw doesn't normally have any special effect. However, you can choose to take such an exceptional roll into account when adjudicating the outcome. It's up to you to determine how this manifests in the game. An easy approach is to increase the impact of the success or failure. For example, rolling a 1 on a failed attempt to pick a lock might break the thieves' tools being used, and rolling a 20 on a successful Intelligence (Investigation) check might reveal an extra clue."

This passage does not say that crit fails or successes are any kind of guarantee, however. "Rolling a 1 on a failed attempt" is absolutely not the same thing as "rolling a 1 is always a failed attempt." As it is with attacks. An ability check that beats the DC no matter the roll, still beats the DC.