It depends on what you label as the climax of the story. In my opinion, the climax of the story is when little Paul rides and rides and finally has the winner to The Derby. His mother rushes home, unusually concerned for him, to find Paul, "in his green pyjamas, madly surging on the rocking-horse." After he calls out that the horse will be Malabar,
"His eyes blazed at her for one strange and senseless second, as he ceased urging his wooden horse. Then he fell with a crash to the ground."
This climax brings Paul down with illness, the name of the much sought-after winner of the Derby, and brings on the falling action of the story.
The falling action in this story is quick; the gardener and Bassett put money on Malabar and win, Paul spends several days very, very ill, and then dies. There isn't much in the way of falling action, but we do see that his horse was the winner, and the end, disasterous results of Paul's obsession with being lucky. His last words on earth speak of that matter: "Mother, did I ever tell you? I am lucky!" This falling action wraps up where the entire story had been leading, and is an tragic statement on the devastating impact that greed can have on a family.