The conversation between human and AI assistant.
If Jon Snow was the son of [...], why did Ned Stark not tell Catelyn Stark about it?
Was there any hint in the show/books that Catelyn suspected something?
Yes, there were a few hints throughout the series that Catelyn may have suspected that Jon was not Ned's biological son. For example, she was always cold and distant towards him. And in the books, she has a dream where she sees Ned holding a baby with "eyes like blue stars," which could be interpreted as a hint towards Jon's true parentage.