A language model is designed to calculate the probability of a sentence by multiplying the conditional probabilities of each word given the words that came before it. For the sentence 'The cat sat', this would be calculated as P('The') * P('cat' | 'The') * P('sat' | 'The cat'). What is the fundamental problem with calculating the probability of the very first word, 'The', in this specific manner?

Applying the Start of Sequence Token

A language model is tasked with calculating the probability of the sentence 'The quick brown fox'. Using the chain rule of probability and a special start-of-sentence token denoted as <s>, how would the model correctly formulate this calculation?