Is this a glitch in Minecraft armor durability?

The phenomenon is not a glitch, it's actually the result of an unintuitive algorithm that is used to calculate your armor points.

It is calculated using the following equation:

The information needed to use the equation are as follows:

Base Armor Points

The following table lists the base armor points of the different armor types. These are the numbers that get plugged into the summation that is the coefficient of the fraction.

               Base Armor Points
Helmet                1.5
Chestplate             4
Leggings               3
Boots                 1.5

The base armor points of a piece of armor are the hardcoded values for the number of armor points it provides when it is has no damage and is the only thing that is worn. They do not vary with differences in the material used to craft the armor, material type only affects durability.

For more details on base armor points refer to the minecraft wiki page on Armor

Base Durability

The following table lists the base durabilities of the different armor types. These are the numbers that get plugged into the summation that is the denominator of the fraction in the armor point expression.

            Leather  Gold  Chainmail  Iron  Diamond
Helmet        34      68      67       136    272
Chestplate    49      96      96       192    384
Leggings      46      92      92       184    368
Boots         40      80      79       160    320

The numbers represent the number of half hearts of damage that each item can absorb before they get destroyed.

For more details on item durability refer to the minecraft wiki page on Item Durability

Current Durability

Current durability is the durability left (counted in half hearts) in the piece of armor in question. It can be estimated by looking at the durability bar that appears underneath damaged pieces of armor. If this bar is not present the armor's current durability is the same as the base durability. If it is present and it appears to be, for example, one quarter of the way full then the current durability is one quarter of the base durability.

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Calculation for the Above Scenario

So the two pieces of armor involved are a undamaged leather chestplate and a pair of boots that look they have been damaged to about an eighth of their base durability.

So first we look up the base armor points and base durabilities of the items:

Base Armor Points:
   Chestplate = 4
   Boots = 1.5

Base Durability:
   Leather Chestplate = 49 
   Leather Boots = 40

Based on the base durabilities we can calculate the current durabilities, which are as follows:

Current Durability:
   Chestplate = 49 * 1 = 49
   Boots = 40 * (1/8) = 5

Plugging all this information into the main equation we get:

Armor Points = (4 + 1.5) * ((49 + 5)/(40 + 49))
             = (5.5) * (54/89)
             = 5.5 * .6
             = 3.3 ≈ 3

This page explains it, it's not simple:

http://www.minecraftwiki.net/wiki/Item_Durability