A fuse is a short. It is just a wire. In normal operation you read no voltage across it because you are just reading two sides of a wire. If the fuse is blown, it becomes an open, two separate wires. One side is connected to your power supply, the other is connected to ground through the rest of your device. Since it is two separate wires and one of those wires is powered you will have a voltage across the fuse.
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