Question

why did the gloom faced man say 'Mr.Easton knows his buissness'?

Answer 1

Miss Fairchild was glaring at the handcuffs. The glum-faced man asked her not to worry as it was Mr. Easton's business as a marshal to handcuff the convict (the glum-faced man) to keep him from getting away.

Answer 2

As miss Fairchild was fascinated by the handcuffs , glum faced man thought that she may find out the truth that Easton is the culprit. So he said that Easton knows his business.