Contrary to popular belief, fat does not turn into muscle. You have fat cells and muscle fibers. Fat cells get filled with the energy you consume but fail to use, and muscles grow when they are strained beyond their usual capacity.
Another thing I hear often is people say “Muscle weighs more than fat.” Question: Which weighs more, a pound of metal or a pound of feathers?” They both weigh a pound, but the density of the two are very different. Take for example, a mushball (fat) and a baseball (muscle). Both weigh about the same, but the density of the baseball is a lot higher and the mushball is a lot bigger. Also, as an added benefit to having muscle, you burn more calories because muscle requires more energy to function properly, as opposed to fat that uses little or no energy to simply exist.