The Police would have heaps of evidence - they don't share very often, and so they shouldn't.
If the police have heaps of evidence, then why are they now whipping out the horses and going for a ride in the park? It seems like that should have been done weeks ago. I think the police don't have a body or handbag, and i even doubt they have a (strong) circumstantial case. I think today was a Hail Mary.