Dynamic downcast on private inheritance within private scope

A tweak on this question that I've run into. Consider:

class A {};

class B : private A {
   static void foo();
};

void B::foo(){
   B* bPtr1 = new B;
   A* aPtr1 = dynamic_cast<A*>(bPtr1); // gives pointer
   B* bPtr2 = dynamic_cast<B*>(aPtr1); // gives NULL
}

Since aPtr1 is, in fact, of type B*, and since we've got full access to B and its inheritance from A, I'd expected both casts to work. But they don't; why? Is there another way to achieve this cast?

Note that:

• If foo() were not a member of B, both casts would fail.
• If B inherits from A publicly, both casts would work.