We don't find out what the conspiracy is. Vanessa Redgrave stumbles in and out of the film almost at random, and revealing nothing. Instead the incident at the park is a tentpole on which to hang various reflections on 60s London. Antonioni is rather sniffy about the rank materialism of the sex, drugs and rock 'n' roll generation. His protagonist Thomas is more interested in the gritty existence of the downtrodden – choosing photographs of old men in doss houses for his book, rather than the silly fashion stuff he's known for. But he's compromised as well, as that famous scene with Verushka demonstrates. His may want his camera to be the window into his soul, but more often it's just another cock.
My spiritual film guide David Thomson describes Antonioni as an "anxious unbeliever". It's true that the empty space and untethered morality in his films suggest the stresses of existentialism. Thomas is searching for the transcendent in art and in life – that one little element that would make the whole make sense (in the words of his painter friend). The death and disappearance in the park provide him with the miracle he needs. I suspect there may be an echo here of Jesus's empty tomb – a brush with faith which Thomas wanders away from.
Instead we end with him alone in the middle of the park, after momentarily being tempted to join an act by a bunch of revelling mimes. The transcendent is replaced with a collective imagining by artists, who seem to be enjoying themselves. Thomas used to be part of that gang, but that last shot sees him isolated from their youthful romps as well. My guess is Antonioni can't let go of his hankering for eternal truths. He finds the postmodern age, where people make their own truths, beguiling, but ultimately dispiriting.