He has no evidence, so he is just grasping at straws.
grasp at straws
idiomTo guess randomly or pursue any apparent option, due to a lack of clear choices or information.
Origin
first recorded 16th c.In reference to a drowning person grabbing any floating object, even a straw, to save themselves. First used by Thomas More in A Dialogue of Comfort Against Tribulation (1534).
With no leads left to follow, the detective began grasping at straws to solve the mystery.
In a desperate attempt to justify his failed policy, the politician grasped at straws, citing irrelevant data from a decade ago.