Learn Swedish: En trolig anledning är brist på bevis. - A likely reason is lack of evidence.

Trolig (likely or probable) is an adjective, and here it modifies the noun anledning (reason). However, it is the exact root word for the sentence adverb troligen (probably). Because the adjective already ends in -lig, Swedish drops the extra 'lig' and just adds -en to form the adverb.

Why is the preposition på used after brist instead of a word for "of"?

In Swedish, the noun brist (lack or shortage) almost always pairs with the preposition på. It is a fixed collocation that you should memorize as a set phrase. You will see it in many common expressions, such as brist på tid (lack of time) and brist på pengar (lack of money).

What is the difference between anledning and orsak, since both can translate to "reason" or "cause"?

Anledning is typically used for a "reason", motive, or justification behind a human action or decision (such as dropping a police investigation due to lack of evidence). Orsak usually refers to a direct, physical "cause" of an event (like a short circuit causing a fire). While they can sometimes overlap, anledning is the most natural fit here.

Is bevis singular or plural in this sentence?