On the Wikipedia page about naive Bayes classifiers, there is this line: 


  $p(\mathrm{height}|\mathrm{male}) = 1.5789$ (A probability distribution over 1 is OK. It is the area under the bell curve that is equal to 1.) 


How can a value $>1$ be OK? I thought all probability values were expressed in the range $0 \leq p \leq 1$. Furthermore, given that it is possible to have such a value, how is that value obtained in the example shown on the page? 

That Wiki page is abusing language by referring to this number as a probability.  You are correct that it is not.  It is actually a probability per foot.  Specifically, the value of 1.5789 (for a height of 6 feet) implies that the probability of a height between, say, 5.99 and 6.01 feet is close to the following unitless value:

$$1.5789\, [1/\text{foot}] \times (6.01 - 5.99)\, [\text{feet}] = 0.0316$$  

This value must not exceed 1, as you know.  (The small range of heights (0.02 in this example) is a crucial part of the probability apparatus.  It is the "differential" of height, which I will abbreviate $d(\text{height})$.)  Probabilities per unit of something are called densities by analogy to other densities, like mass per unit volume.

Bona fide probability densities can have arbitrarily large values, even infinite ones.



This example shows the probability density function for a Gamma distribution (with shape parameter of $3/2$ and scale of $1/5$). Because most of the density is less than $1$, the curve has to rise higher than $1$ in order to have a total area of $1$ as required for all probability distributions.



This density (for a beta distribution with parameters $1/2, 1/10$) becomes infinite at $0$ and at $1$.  The total area still is finite (and equals $1$)!



The value of 1.5789 /foot is obtained in that example by estimating that the heights of males have a normal distribution with mean 5.855 feet and variance 3.50e-2 square feet.  (This can be found in a previous table.) The square root of that variance is the standard deviation, 0.18717 feet.  We re-express 6 feet as the number of SDs from the mean:

$$z = (6 - 5.855) / 0.18717 = 0.7747$$

The division by the standard deviation produces a relation

$$dz = d(\text{height})/0.18717$$

The Normal probability density, by definition, equals

$$\frac{1}{\sqrt{2 \pi}}\exp(-z^2/2)dz = 0.29544\ d(\text{height}) / 0.18717 = 1.5789\  d(\text{height}).$$

(Actually, I cheated: I simply asked Excel to compute NORMDIST(6, 5.855, 0.18717, FALSE).  But then I really did check it against the formula, just to be sure.)  When we strip the essential differential $d(\text{height})$ from the formula only the number $1.5789$ remains, like the Cheshire Cat's smile.  We, the readers, need to understand that the number has to be multiplied by a small difference in heights in order to produce a probability.
