which the assignment of values to some beables $\Lambda $ implies, not necessarily a particular value, but a probability distribution $Pr(A|\Lambda )$, for another beable $A$. Here is how Bell (\[2004, p. 54\]) defines it (in my notation):

> Let $N$ denote a specification of *all* the beables, of some theory, belonging to the overlap of the backward light cones of space-like separated regions 1 and 2. Let $\Lambda $ be a specification of some beables from the remainder of the backward light cone of 1, and $B$ of some beables in the region 2. Then in a *locally causal theory* $Pr(A|\Lambda
> ,N,B)=Pr(A|\Lambda ,N)$ whenever both probabilities are given by the theory.

If $M$ is a specification of some beables from the backward light cone of 2 but not of 1, then (assuming the joint probability distribution $Pr(A,B|\Lambda ,M,N)$ exists)$$\begin{aligned}
Pr(A,B|\Lambda ,M,N) &=&Pr(A|\Lambda ,M,N,B).Pr(B|\Lambda ,M,N)  \label{1} \\
&=&Pr(A|\Lambda ,N).Pr(B|\Lambda ,M)  \label{2}\end{aligned}$$where (\[1\]) follows from the definition of conditional probability, and (\[2\]) follows for any locally causal theory. This means that any theory of local beables that is locally causal satisfies the condition$$Pr(A,B|\Lambda ,M,N)=Pr(A|\Lambda ,N).Pr(B|\Lambda ,M)  \label{3}$$

In his 1990 presentation Bell modified his formulation of local causality, in part 