TCP packets have a sequence number and if the sequence number is less than the receiving computer is expecting, the kernel will discard the packet. In fact, since so many people are behind DHCP, the discarding is probably going to happen at that level, and the actual computer will never see the second packet.
This makes the most sense. The idea is to hijack the connection and insert packets into the stream which override the original packets, due to arriving first. That's why latency matters so much.
