I had a question about Tor and the anonymity status of a fully decrypted packet that leaves a Tor exit node. My high-level understanding is that prior to a packet traversing the Tor network, a Tor client chooses 3 Tor relay nodes for the packet to go through and encrypts a packet with the exit node's public key, then encrypts the encrypted packet with a middle node's public key, then does it again with the entry node's public key. And each node decrypts the packet as the packet arrives to it.
This is the part where I don't understand how this process achieves anonymity. After the Tor exit node fully decrypts a packet, that packet will be a normal packet so it should have a source address and a destination address. Therefore anyone who sniffs a packet after it leaves a Tor exit node will know what the source address and what the destination address is, right?
There must be something I don't understand about the The Onion Routing process and I was hoping somebody would help me with understanding how is the packet anonymous after it leaves the exit node. After all since it has been fully decrypted, its source and address fields can be sniffed just like any other packet?