We have to put an article there, either 'a', 'an' or 'the' there because without it, the meaning changes.
For example;
Roses are red,
violets are blue.
Sugar is sweet,
and so are you.
And so if you put;
Happiness is ability.
That sentence just makes me go huh???
It just doesn't make much sense.
The pattern here is:
the <something> to <something>
E.g.
1. Can you show me
the way to the shop?
2. Hatred is
the path to the darkside.
3. I no longer have
the strength to fight.
However, sometimes you can use a/an in place of the. For e.g.
1. There are many ways to the shop.
So, can you show me
a way to the shop?
2. There are many paths to the darkside. Hatred is
a path to the darkside.
3. Here your only option is 'the'.
So in this case:
Happiness is
the ability to <something>
The meaning changes a little bit if you use 'an' instead of 'the'. You can't leave out the 'the' because it's confusing.
Consider;
Anger and hatred are paths to the darkside.
and
Anger and hatred are the paths to the darkside.
1st one means that there might be other paths to the darkside other than anger and hatred.
The 2nd one means anger and hatred is all.
Well, at least that's how I interpret it.