Why does hamlet believe that altering the murder of gonzago will provide proof of claudius's guilt

He leaned his head against the wall; his eyes were shut, his hands clasped in each other, and his body seemed to be sustained in an upright position merely by the cellar-door against which he rested his left shoulder. the lethargy into which he was sunk seemed scarcely interrupted by my feeling his hand and his forehead. his throbbing temples and burning skin indicated a fever . . there was only one circumstance that hindered me from forming an immediate determination in what manner this person should be treated. my family consisted of my wife and a young child. our servant-maid had been seized, three days before, by the reigning malady, and, at her own request, had been conveyed to the hospital. we ourselves enjoyed good health, and were hopeful of escaping with our lives. our measures for this end had been cautiously taken and carefully adhered to. they did not consist in avoiding the receptacles of infection, for my office required me to go daily into the midst of them; nor in filling the house with the exhalations of gunpowder, vinegar, or tar. they consisted in cleanliness, reasonable exercise, and wholesome diet. who is the story’s first-person narrator