Equation 1 from the link is used to determine the probability for one production rule. Assume we have data that we can use for estimating these probabilities; i.e. we believe in the distribution of this data.
Then, to estimate the probability of $X \rightarrow \lambda$, use the following formula:
$$
P(X \rightarrow \lambda) = \frac{c(X \rightarrow \lambda)}{\sum_{\mu}c(X \rightarrow \mu)}
$$
where $c(X \rightarrow \lambda)$ is the number of times we observed $X$ producing $\lambda$ in the data; $\sum c(X \rightarrow \mu)$ is the number of times we observed $X$ producing $\mu$, for any $\mu$ in the data.
Thus, the denominator of the above equation becomes the number of times $X$ produces any symbol in the data, normalizing the probabilities for each left hand side of the production rule. Note, in Figure 1 of the link, the sum of the probabilities equals one for any symbol on the left hand side of the production rules.
For example, let us say that $G$ appeared on the left hand side of a production rule 10 times in the data. We observe that 8 out of these 10 times $G$ produced $J$. We also observed that $G$ produced $Hf$ and $bfffH$ once. Thus, $\sum_{\mu} c(G \rightarrow \mu) = 8 + 1 + 1 = 10$, $c(G \rightarrow J) = 8$, $c(G \rightarrow Hf)$ = 1, and $c(G \rightarrow bfffH) = 1$. Hence, we compute the probabilities to be:
$$
P(G \rightarrow J) = \frac{8}{10} = 0.8\\
P(G \rightarrow Hf) = \frac{1}{10} = 0.1\\
P(G \rightarrow bfffH) = \frac{1}{10} = 0.1
$$
We can do the same for $H$. Say that we observed $H$ on the left hand side 4 times, producing $l$ and $lH$ two times each. The probabilities for both of these productions rules is then $\frac{2}{4} = 0.5$.
