Cover & Thomas textbook notation Exercise 2.27 in Elements of Information Theory (2nd ed.) reads:
Let $\mathbf{p} = (p_{1}, p_{2}, \ldots, p_{m})$ be a probability
  distribution on $m$ elements (i.e., $p_{i} \geq 0$ and
  $\sum_{i=1}^{m} p_{i} = 1$).  Define a new distribution $\mathbf{q}$
  on $m - 1$ elements as $q_{1} = p_{1}, q_{2} = p_{2}, \ldots,
  q_{m-2} = p_{m-2}$, and $q_{m-1} = p_{m-1} + p_{m}$ [i.e., the
  distribution $\mathbf{q}$ is the same as $\mathbf{p}$ on $\{1, 2,
  \ldots, m - 2\}$, and the probability of the last element in
  $\mathbf{q}$ is the sum of the last two probabilities of
  $\mathbf{p}$].  Show that
  $$
    H(\mathbf{p}) = H(\mathbf{q}) + (p_{m-1} + p_{m})H\left(
      \frac{p_{m-1}}{p_{m-1} + p_{m}}, \frac{p_{m}}{p_{m-1} + p_{m}}
    \right).
  $$
Question 1. What does $H\left(
      \frac{p_{m-1}}{p_{m-1} + p_{m}}, \frac{p_{m}}{p_{m-1} + p_{m}}
    \right)$ mean in this context? 
Question 2. Where is this notation introduced in the text?
Please do not provide a solution to the exercise.
 A: To define the entropy $H$, all you need is a probability distribution; that is, a vector of nonnegative real numbers summing to $1$. In this case, it happens to be the vector $\mathbf r = (a,b)$ with
$$
a := \frac{p_{m-1}}{p_{m-1}+p_m}, b := \frac{p_m}{p_{m-1} + p_m}.
$$
Note that before defining $H(\mathbf r) = H(a,b)$, you must still verify that $\mathbf r = (a,b)$ is a well-defined probability distribution. That is, you should check that:
$a \geq 0, b \geq 0$, and $a+b = 1$. (Easy exercise!)
Added: The OP remarked that the book defines $H(X)$ for a random variable $X$, but not $H(\mathbf p)$ for a distribution vector $\mathbf p$. So as per @Didier's comment below, I will explicitly say what this means. Apparently, the book does define the notation after all; see the comments below. Originally I had defined the notation $H(\mathbf p)$ explicitly; I will just keep it in my answer. 
For a probability distribution $\mathbf p$, we can define $H(\mathbf p)$ by the familiar Shannon formula:
$$
H(\mathbf p) := \sum_{i=1}^{n} p_i \log_2 \left(\frac{1}{p_i}\right).
$$
We can also relate this definition to the entropy of a random variable. Imagine a random variable $X$ with support $\{ 1,2, \ldots, n \}$ such that $\Pr[X = i] = p_i$. Then directly from the two definitions, we see that $H(X)$ is equal to $H(\mathbf p)$. 
