How was Barker caught in a trap by Holmes? Which strong evidence were explored

After questioning Barker and Mrs. Douglas, Holmes asks Ames to come in. He inquires what shoes Barker was wearing the night of the murder. Ames responds that he was wearing house slippers. Holmes finds the slippers and looks on the bottom. They are covered in blood, and the mark of the window matches that of the sole of the slipper. The men are all astonished.