The reason I can believe that you are are conscious and have free will is because I perceive myself to have consciousness and free will (well, somewhat), and I can imagine how I could have just as easily been born in your shoes. So we can see how our belief in consciousness depends on a sense of empathy.
Empathy can be understood as a symmetry in existence and feeling. Symmetries correspond to preserved quantities in physics:
- translational spatial symmetry ←> conservation of momentum
- rotational spatial symmetry ←> conservation of angular momentum
- symmetry in time ←> conservation of energy
Similarly, symmetry in our perception of reality corresponds to the size of your empathetic circle, and the consciousness you ascribe to other beings. Can you imagine yourself as a pig? How about an insect? How about a rock?