Collecting into a Vec is so common that slices have a method to_vec that does exactly this:
let b = a.to_vec();
You get the same thing as CodesInChaos’s answer, but more concisely.
Notice that to_vec requires T: Clone. To get a Vec<T> out of a &[T] you have to be able to get an owned T out of a non-owning &T, which is what Clone does.
Slices also implement ToOwned, so you can use to_owned instead of to_vec if you want to be generic over different types of non-owning container. If your code only works with slices, prefer to_vec instead.