How certain are you? Modal deductions
Modal verbs can express certainty rather than obligation or ability. Müssen can signal a strong deduction; könnte expresses a possibility. To infer something about the past, use Partizip II plus haben or sein.
Understand the idea
Modal verbs can express an assessment of likelihood rather than permission or obligation. Müssen can signal a strong inference; könnte can present a possibility. Context tells the reader whether a modal is being used in this evidential sense.
Build it step by step
Combine the modal with an infinitive for a present inference. To make an inference about a completed event, use a perfect infinitive such as participle plus haben or sein. Choose wording that matches the strength of the available evidence. Other modals can express different degrees or kinds of assessment.
See it in a sentence
Das Licht brennt. Er muss noch im Büro sein.
Du hast kaum geschlafen. Du musst müde sein.
A useful memory aid
Restate the meaning in English first: it must be so, or it could be so. Then choose the German modal that conveys that confidence.
A common trap
Do not read every müssen as an instruction. Conversely, do not use a strong deduction when the context only supports a tentative possibility.