To predict the next word using a Probabilistic Context-Free Grammar (PCFG), the conditional probability of the next word $$w_i$$ given the preceding words is calculated as the ratio of their prefix probabilities:

$$P(w_i | w_1, w_2, ..., w_{i-1}) = \frac{P(w_1, w_2, ..., w_{i-1}, w_i)}{P(w_1, w_2, ..., w_{i-1})}$$

Carleton College

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PCFGs are useful in language modeling as they can predict the probability of a sentence or part of a sentence

PCFGs for Language Modeling

An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

Speech and Language Processing (3rd ed. draft) 

In a Probabilistic Context-Free Grammar (PCFG), the probability of an ambiguous sentence is the sum of the probabilities of all valid parse trees for that sentence:

$$P(S) = \sum_{T \text{ s.t. } S=\text{yield}(T)} P(T)$$

Probability of an Ambiguous Sentence in a PCFG

In a Probabilistic Context-Free Grammar (PCFG), the probability of an unambiguous sentence is simply the probability of the single valid parse tree for that sentence: $$P(T,S) = P(T)$$

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