I am trying to understand this concept and it just isn't clicking. Any help would be appreciated!
It is worse than you state here, in that, for Hume, causality is not only merely probabilistic, it does not have a real existence at all, but is supplied by us in the form of a sentiment inspired by observing concatenations of events and forming expectations for certain sequences based on previous observations.
For Hume there is no idea of a necessary connection because there is no impression from which that idea can be copied. He spends the entirety of Section VII of An Enquiry Concerning Human Understanding searching for the impression of a necessary connection between physical objects, between the human body and the human consciousness, and between ideas themselves, and he comes up empty in each case. Since these cases exhaust the ontological possibilities, Hume concludes that there is no such impression, but rather an internal impression of our own expectation of an event from which we mistakenly derive the idea of a necessary connection.
In Section IV of the Enquiry, Hume argues that only relations of ideas can be known through demonstration and can therefore be shown to be necessary truths. Such relations of ideas can be identified by negating the propositions asserting them and seeing that the negations assert contradictions: The interior angles of a triangle add up to 180 degrees. Since one definition of a triangle is "a plane figure, whose interior angles add up to 180 degrees," it would be a contradiction to assert The interior angles of a plane figure, whose interior angles add up to 180 degrees, do not add up to 180 degrees. This contradiction, created by negating the original proposition, shows us that it is a relation of ideas.
However, when we negate a statement of cause and effect: The wind toppled the tree turns into The wind did not topple the tree. The negation of the original proposition is as logically possible as the original proposition. This circumstance shows us that it is a matter of fact, whose truth value can only be known empirically. A proposition whose truth can only be known empirically can only be known probably. A priori or demonstrative reasoning is necessary while a posteriori or matter-of-fact (empirical) reasoning is probable.
Hume asserts this oracularly in Sections III and IV of the Enquiry, but argues in Sections IV and VII that no sort of reasoning can link one object to another or one event to another: "So that, upon the whole, there appears not, throughout nature, any one instance of connection, which is conceivable by us" (Enquiry, Sect VII, Part II).