I think he's banking on something that seems unlikely to me, but I guess he'd know better. Anyway, the way the nominating process works is that delegates are sent to the Republican National Convention and for the first round of votes they have to vote along the lines that their state voted (either winner take all or split along percentages for each candidate). However, and especially if all four remain until the convention, the first vote won't give anyone enough to get the nomination.
For all subsequent votes the delegates don't have to vote according to how the people in their states voted and can cast for whoever they like. No delegates have actually been chosen yet and Paul is hoping to get a majority of delegates who back him, so even if he doesn't win outright, he can get the nomination on the second or third vote. Furthermore, I'm not sure exactly, but I think when a candidate drops out any delegates he had won are now free to vote however they like.
Also, as an aside, with the ridiculously unconstitutional things both parties' candidates are proposing, even if Paul wasn't nominated, I'd love to see him as an Independent to act as a mediating voice in debates.