What happens when Catelyn uses her ability against a character with intimidate?

Does

a) said character not count its strength for purposes of determining winner but still count for intimidate, or
b) said character has effectively no strength for the purpose of intimidate (i.e. cannot intimidate any character)

Catelyn Stark:
Response: After Catelyn Stark is declared as a defender, choose a participating character. For the duration of the challenge, that character does not count its STR.

Catelyn doesn't remove, lower or modify STR. She simply says "you don't contribute when we tally up the sides to see who wins."

Intimidate does the same thing for all characters with a lower STR than the Intimidate character. He's still got his STR, he just doesn't count it toward winning the challenge.

Essentially, Catelyn has no affect on Intimidate. So a whole lot of participants may not be counting STR in this challenge.