A machine is built to make mass-produced items. Each item made by the machine has a probability $p$ of being defective. Given the value of $p$ , the items are independent of each other. Because of the way in which the machines are made, $p$ could take one of several values. In fact $p=X/100$ where $X$ has a discrete uniform distribution on the interval [0, 5]. The machine is tested by counting the number of items made before a defective is produced. Find the conditional probability distribution of $X$ given that the first defective item is the thirteenth to be made.  