For what it’s worth, I think more people believe in free will than don’t.
So the average person, by the literal meaning of average, does believe it.
I acknowledge that you said define, not believe - and to this I say,
I think most have not defined ‘free will’ in their own terms, but have accepted the concept that was taught to them - the general definition.
All one’s desires are animal desires, as we are animals - but this is pedantic.
You likely mean, ‘base animal desires’ - those that aren’t enlightened by logic / reason / deeper understanding.
A lot of one’s desires aren’t necessarily in conflict,
and can be guided and pruned, with one’s reason, towards wise behavior without compromising the initial instinct.
One however cannot chase every desire to it’s maximum extent without compromising other desires.
For example, one may desire to eat excessive amounts of food - but also desire to be healthy.
These two desires demand compromise - otherwise one desire will be neglected, producing dissonance.
With wisdom though, we can find a path balancing these desires - such that we meet a satisfactory equilibrium.
Determinism isn’t necessary to constrain base animal desires.
One can be an atheist, and still have the will to live in a way guided by reason -
not mindlessly chasing urges without any consideration towards the myriad of cascading consequences.
I believe we are born with preferences that can be utilized towards compassionate behavior,
that is authentic to our ‘nature’ / to our structure - enabling us to live a wise, ethical and fulfilling life.
We are a social animal. We evolved working as a cooperative unit.
Our structure does not demand of us that we ought be each other’s enemies.
A lot of our more violent tendencies are products of scarcity and non-mutual success.
Where two parties, due to their circumstances, have needs at the expense of the other.
Despite what we may be taught, this needn’t be applicable to our species currently.
We can coexist - if we were to change our expectations and ideals towards what a preferred society looks like.
Many aren’t doing this - thus, the conflict and the violence continues.
This is isn’t an indication of what our species is capable of -
but an indication of how we react to pretty dismal circumstances.
We ain’t saints, but can get close if we tried.
All that being said:
If one believes in determinism,
one can try to find the silver linings.
Try to find ways to utilize this information.
Not every truth is convenient,
and some believe things that inconvenient -
not because they want it to be the case,
but because their judgement concludes it to be the most likely case.
Not everyone who lacks belief in the credibility of free will,
desires that they have no free will - some do, sure, but not all.