In reading Blake Master's notes on Peter Thiel's lecture on start ups, I came across this metaphor of the technology frontier:
Picture the world as being covered by ponds, lakes, and oceans. You’re in a boat, in a body of water. But it’s extremely foggy, so you don’t know how far it is to the other side. You don’t know whether you’re in a pond, a lake, or an ocean.
If you’re in a pond, you might expect the crossing to take about an hour. So if you’ve been out a whole day, you’re either in a lake or an ocean. If you’ve been out for a year, you’re crossing an ocean. The longer [the] journey, the longer your expected remaining journey. It’s true that you’re getting closer to reaching the other side as time goes on. But here, time passing is also indicative that you still have quite a ways to go.
My question: is there a probability distribution or statistical framework that best models this situation, especially the bolded part?