Price ranged advised by mindacos:

http://i.imgur.com/YqKGoHv.png

Only 2 in existence forever. The sales listed below are only from one Billy as the other Billy hasn't left the owner's backpack in 400+ days.

Sale 1

https://backpack.tf/profiles/76561198301176237#!/compare/1498435200/1498608000

Sold as part of an exchange. Omitting the value of parts on the Ambassador. Pro KS SF Ambassadors are selling for 7 keys.

67.5 (value of burning billy) - 7 (value of ambassador) - 4 (the keys) = 56.5 or 57 (rounded up, value of PS Billy in this case)

Sale 2

https://backpack.tf/profiles/76561198087390671#!/compare/1499558400/1499817600

Sold for mixed. Paid 48 keys + Circling Hearts A Hat to Kill For (27 - 32) = 75 - 80 keys, 77.5 or 78 (rounded up, value of PS Billy in this case)

Thanks guys! =)