What is the actual durability of an Unbreaking tool?

In Minecraft, the "Unbreaking" enchantment causes tools to last longer, but the exact durability of these tools is something that I have failed to find.

By using F3 + H I have found that the durability counter of the item does not change. The only thing I have noticed is that it will not decrease for a few broken blocks. Is there an actual value for how long each "Unbreaking" enchantment will last?

As correctly noted by Thorsal, the durability of an 'Unbreaking' item is not fixed, but depends on chance.

More specifically, the number of uses you will get out of a given tool will follow a binomial distribution. This is the same statistical law that predicts things like "how many heads will I get out of 100 coin tosses?"

Consider that a diamond pickaxe normally has durability of 1,536 uses. If you plot the binomial probability density function (PDF) for 1,536 'successes' with a 'success rate' of P = 1/2 = 0.5 (Unbreaking 1), P = 1/3 = 0.333 (Unbreaking II), and P = 1/4 = 0.25 (Unbreaking III) you get the following graph:

This shows that an Unbreaking III Diamond Pick will last, on average, about 6,144 uses (four times as long as a normal Diamond Pick.) However there is also a chance it will break after only 6,000 uses. Similarly, there is a chance it will last for 6,500 uses.

However there is basically no chance it will last longer than 7,000 uses, or less than 5,000 uses.

According to the Wiki:

For most items, (100/(Level+1))% chance a use reduces durability. On average, lifetime is (Level+1) times as long.

In other words, the actual durability on an item with the Unbreaking enchantment depends on chance and is no longer a fixed value.

This accounts for your observations that the durability didn't decrease and also the re-appearing of at tool you've just broken when you equip a similar tool in your hotbar.