Distribution conditional on the Sum of IID Normals

Question

Assume I have iid $\varepsilon_{i}\sim \mathbb{N}(0,1)$ for $i=1,\dots,T$,

What is the marginal distribution of $\varepsilon_{i}$, conditional on $\sum_{i=1}^{T}\varepsilon_{i}=C$, i.e

$$ F(\varepsilon_{i}|\sum_{j=1}^{T}\varepsilon_{j}=C) $$

Thanks!