Can we estimate Max and Min of the $\frac 12 . P (B\mid A). P (C\mid A\;\text{and}\; B)$ for $3$ independent events $P(A)=P(B)=P(C)=\frac 12$?

Question

I have three dependent events $A,B,C$, each one happens with probability $\frac 12$. I want to estimate the following probability $$ P_{tot}=P (A\;\text{and}\; B\;\text{and}\; C)=P (A) \cdot P (\;B\;|\;A\;) \cdot P (\;C\;|\;A\;\text{and}\; B\;) \\ \qquad\qquad\qquad\qquad\qquad=\frac 12 \cdot P (\;B\;|\;A\;) \cdot P (\;C\;|\;A\;\text{and}\; B\;) $$

If I do not have any other information, can we estimate the minimum and maximum value that $P_{tot}$ might have? Does the ordering of the events affect the probability?