What are the reasons that Langdon and Sophie suspect that Jacques passed on his secrets to them as stated in Chapters 59 through 63?

Langdon and Teabing learn from Sophie that, in fact, Sauniere was the Grand Master of the Priory. Langdon then tells Teabing his and Sophie's assumption of why Sauniere had to pass on the secret to someone outside the circle--because the other three members of the circle had been murdered too, and if Sauniere did not pass his secret to Sophie and Robert, the Grail would be lost forever.