Observe them closely for the next three weeks - if no shouting, sticky,wet backend and wagging their tails (esp if billy is still on the holding), then you should assume they are in kid. You could get them scanned, but not all vets/scanners will be able to do this. Also not sure how reliable it is with goats, esp with inexperienced scanners.
You would probably also have to take them either to the vets (if he has a set-up for scanning) = expensive or go round when the local scanner is doing your nearest farmer. the timing could all be wrong and you could introduce disease. IMHO not worth the trouble.