99% of broken spokes are down to too low tension. The problem is flexing - with tension too low, the spokes can flex at the elbow, this flexing causes fatigue and eventually snaps spokes. Since the spokes fatigue at similar rates, if one goes then the rest are going to go soon. My general recommendation is that if more than two spokes snap in a wheel, it's time to rebuild with all new spokes.
This, except it's not just 'at the elbow' as a couple of weeks ago I had two go in my straight-pull spoked front wheel on a night ride. Took it to my local chap and he put two more in - and others snapped as he tensioned up.
His recommendation - full rebuild with new spokes.
Although in the OP's case it may not be worth it with that rim/hub combo - new wheel maybe more 'economical'.