Implication of an Impossible Initial Event

A language model calculates the probability of a sequence of three tokens, {x₀, x₁, x₂}, using the formula: Pr(x₀, x₁, x₂) = Pr(x₀) * Pr(x₁|x₀) * Pr(x₂|x₀, x₁). If the model determines that the initial token, x₀, is an impossible event, what is the joint probability of the entire sequence?

Consequence of an Impossible Starting Token

A language model is calculating the probability of the sequence 'Zxq#w the cat sat'. If the model's vocabulary does not contain the token 'Zxq#w', making its initial probability zero, the model can still assign a non-zero probability to the entire sequence by considering the high probabilities of the subsequent words 'the', 'cat', and 'sat'.