Which is the difference between $P(A \mid B)$ and $P(A=t \mid B)$ in a Bayesian Network?

Question

Which is the difference between $P(A \mid B)$ and $P(A=t \mid B)$ in a Bayesian Network, where $A$ and $B$ are boolean values?

Answer 1

I would say that the difference is merely that the first one denotes a probability mass function and the latter denotes just a probability, that is a value. For instance

$$ P(A|B)=\begin{cases} 1/3 \mbox{ if A is true}\\ 2/3 \mbox{ if A is false}\end{cases} $$ and hence $$P(A=t | B)=1/3.$$

It does not appear to have anything to do with Bayesian theory.