Is it possible to not pay a conditional counter with the cost set at 0?
Rule 117.5 states:


  117.5. Some costs are represented by {0}, or are reduced to {0}. The action necessary for a player to pay such a cost is the player’s acknowledgment that they are paying it. Even though such a cost requires no resources, it’s not automatically paid.


So, it is possible to refuse to pay an optional payment with a cost of 0 mana, and a person can counter their own spell by refusing to pay the cost of 0 mana.