Learn Danish: Morderen vil sandsynligvis efterlade et bevis. - The murderer will probably leave a piece of evidence behind.

You are right that vil usually means "want to". However, in this lesson we are learning how to use modal verbs to express probability (their epistemic use). Here, vil is used to make a prediction. It doesn't mean the murderer has a desire to leave evidence, but rather that it is likely to happen, exactly like the English "will".

Is there a trick to remembering the long word sandsynligvis?

Yes, breaking it into its three parts makes it much easier to remember. Sand means "true", synlig means "visible", and the suffix -vis is like the English "-ly" or "-wise". Put them together and it literally means "in a truly visible way", which Danish uses to mean "probably" or "likely".

Why does the English translation say "a piece of evidence" when the Danish just says et bevis?

In English, the word "evidence" is uncountable, so you have to add "a piece of" to count it. In Danish, et bevis (which can also mean "a proof") is a normal, countable noun. One piece of evidence is et bevis, and multiple pieces of evidence would be beviser.

Could I use just lade instead of efterlade to mean "leave"?