Provis tells Herbert about his wife who killed another woman because the other woman showed interest in Provis. His wife then told Provis that she was going to kill their little girl. Mr. Jaggers was the wife's lawyer, and Provis never saw his little girl again. Provis says it was Pip's good deed those years ago and his approximate age of his little girl that moved him to become Pip's benefactor. Based on the story Provis tells, Pip now knows that Provis is Estella's father.
Pip goes to Mr. Jaggers to verify the story, and Mr. Jaggers tells him he never knew who Estella's father was. Jaggers doesn't want to come right out and tell Pip, but he confirms the story by giving Pip a hypothetical situation. Pip is now able to put the pieces together about Estella's parents. Mr. Jaggers advises Pip not to share his information with anyone because it would serve no purpose.