Point Division in Elliptic Curve Cryptography?

Point Division in Elliptic Curve Cryptography?

I want to implement a crypto protocol using Elliptic Curve Cryptography.
However, it requires a division which I cannot handle.
In multiplicative notation, it requires:
Let $\mathbb{G}=\left \langle g \right \rangle$ be a finite cyclic group
of prime order $p$.
select $P \in_{R} \mathbb{G}$ and $a \in_{R} \mathbb{Z}_{p}$ and
compute $S=P^\frac{1}{a}$.
In conversion between multiplicative and additive group notation, I
learned that $S=P^\frac{1}{a}$ means $S=\frac{1}{a}P$ in additive
notation. I only know point addition and point multiplication. Is there a
way to calculate S?