This is an interesting question. As we see from the answers so far, everyone has their take on it. So herewith mine, with the caveat that I'm limiting myself to African animals).
Leopard is without a doubt a hunt with one of the lower chances of success. A number of things have to come together including, but not limited to, the time of year, the amount of game in the area, how recently a cat was taken from the area, the wind conditions, etc. In my case, it took me two hunts to connect.
Dealing with the more esoteric game, I think both bongo and Lord Derby Eland can be challenging, but given that these are usually the primary targets of those hunts, and you likely have at least two weeks to connect, the chances of success are actually pretty high. You just might have to work hard. In my case, 12 days to get a bongo, but an LDE on day 1. The LDE hunter after me struggled and it took him over 12 days to connect.
I'd put mountain nyala in the same bucket. You will have to hunt hard, focussing on just that one animal, but if you do that, in the 14 or more days you will be hunting, you've got pretty good odds of connecting.
Note that if you only had a few days to devote to any of these animals, your odds of success drop precipitously.
Now, hit or miss (so to speak). Forest sitatunga can be exceptionally difficult to find, because there is no plan other than trying to be at the right place at the right time (ie., be at a swamp when a sitatunga is there). Some people I've been told about by my PH's have taken three or more hunts to connect. Far below 50% chance. Other sitatunga will be easier. Giant forest hog or Red River hog can be a very challenging hunt, although they're rarely the focus of a hunt - which is a good thing because I'd give you a less than 50% chance of connecting.
The nocturnal animals can be difficult. I know some who have hunted for serval multiple times and have never seen one. I got one on the first day of a hunt and then never saw another one after that. Brown hyena is a tough hunt and success is far from assured. Honey badger can be tough, but they do come to bait, so if you're patient and in a good area, your chances are pretty good. Caracal without hounds will be less than 50%. I'd say the key to hunting these animals is to hunt the right area, of course, but to hunt with a PH who is experienced in nocturnal animals. From spotting to shooting you generally have very few seconds, so the PH has to be sure very quickly; anyone who has to spend time finding a small animal in a scope will have serious difficulty.
Any rain forest animals which will not bay to dogs are very difficult - less than 50% without a doubt. Dwarf forest buffalo is an example. Forest elephant (L. cyclotis) can be a bit easier, but I would still say less than 50% unless you dedicate an entire hunt and are in a good (unpoached) area (of which there are ever fewer). The various forest duikers, somewhat dependent on the species you're after, can be less than 25%, even if you are dedicated.
To sum up, everything depends on the animal you're looking for, the place you're looking for it, and most importantly, the amount of time you're prepared to dedicate to finding it.
