That's simple, when calculating possibility you just multiply percentage of enchanting that many times thet you are trying to get. So +3 is safe enchant, that's why to get +8 there is a 5 attemts.
So 0,6x0,6x0,6x0,6x0,6 = 0,07(7) which is closer to 8% - my bad. So each time when you trying to get it from +3 to +8 you have only 8% chance to get it. That's why it is so hard even if 60% sounds nice
(knowing that I always try to buy it from the market instead of gamble, but hey that's the game made for isn't it? )