Ability

The word "Ability" means the fact that somebody is able to do something. It also means the skill that somebody possesses. Notice in both the definitions that the word Ability has a sense of capacity in it. Consider this sentence:

This machine has the ability to demolish walls in just a second.

In the above sentence, the word Ability is used in terms of "capacity" and "feature". Surely, the machines do exhibit their capacity (the extent of bearing load) when they perform a task, but let's take a brief look at the word feature. The feature of the non-living thing is its "built-in functionality", or - in anthropomorphic terms - the feature of the non-living thing is its "natural ability". We can rephrase the sentence in the following manner:

This machine has the built-in functionality to demolish walls in just a second.

Do you think that the meaning has changed now, even if by the minutest fraction?

I think the meaning is same - the focus or context differs. I would prefer to probably use the first sentence in the contexts where I am emphasising the power of the machine; whereas, I will use the second sentence in the contexts where I am emphasising the built-in feature of the machine.The word "built-in" suddenly comes into focus, which to some extent reduces the machine to a mere tool. In the first sentence, the machine stands grand.

So, from these two examples we gather that using a synonym does not always do the job - some words are irreplaceable due to many reasons, like the vastness of semantic space as illustrated above. The word Ability is a package word that contains not only the meanings but also a little power to exalt a non-living to a living (at least, it gives such a feeling to the non-living).

The word Ability also covers the intelligence aspect. If you search a thesaurus, it will also list the word Intelligence as its synonym. This is because Ability is not just limited to the physical capacity of doing physical tasks, rather it also refers to the abstract powers (the spiritual and mental powers), which is also the reason that it can subtly exalt the non-living.

Only Ali has the ability to defeat the Chess master.

Now, here the word Ability contains three meanings - the capacity of bearing the load, the intelligence, and the skill required to defeat the Chess master. And the capacity, intelligence and skill are here discussed in their considerable degree. 

It might seem at first sight that Intelligence and Skill are the same, but it isn't so. The word Skill has a different semantic space than Intelligence. Skill is the grand total of all the powers (intellectual, emotional, physical) to do a certain task; whereas, Intelligence is the intellectual power to use that skill. Skill is the substrate for the Intelligence on which it performs its action, without skill intelligence is reduced to half. An intelligent person with no chess skills has lesser chances to win than an intelligent person with the chess skills. If you are thinking that developing skills extempore is a child's play for an intelligent person, then my friend you are terribly mistaken. Developing a skill set is a matter of smart work and experience, which is a process that might not even require higher intelligence levels.

Winning the game against the Chess Grand Master does not require as much intellect as it requires the skill. And this is where the word Genius takes its own route. A Genius is a person whose intelligence is his greatest. He is supremely adept at maneouvering his intelligence to solve the problems without the need of skills. His intellect, in a soft and calm manner, does all what the highest degree of skill can do for any grand master. Intelligence once has gained the boost no longer requires experience as its only source.