Riddle me this

Spoiler Warning

Can someone please explain to me how the Elder Wand passed to Draco Malfoy? (Maybe I’ll post this as a question on Facebook and see what I get there.)

Update: Alrighty, I figured it all out. Draco defeated Dumbledore on the Astronomy tower by disarming him with the Expelliarmus charm, Dumbledore’s wand was flung “in an arc over the edge of the ramparts”. Severus Snape did indeed killed Dumbledore, hitting him “squarely in the chest” with the Avada Kedavra curse, “and then he fell slowly backwards, like a great rag doll, over the battlements and out of sight.” But the wand had already passed to Malfoy. Then, after Dobby caused the chandelier in the Malfoy Manor, “Draco doubled over” and Harry “wrested the three wands from Draco’s grip”. One of which was Draco’s own wand. Thus, Harry defeated Draco by disarming him. Shall I continue?