Translation guide
A rhetorical question expressing that the speaker has no way of knowing the answer, often with irritation or exasperation. In Japanese, this is typically expressed with set phrases rather than literal translations.
Express that the speaker cannot possibly know the answer, often with annoyance.
Very blunt and rough. Used mostly by men in casual, irritated contexts. Literally 'Know? (sarcastic)'.
How should I know where that guy is?
Common casual phrase meaning 'I don't know (and don't expect me to)'. The よ adds emphasis and can sound dismissive.
How should I know about that?
Stronger than 知らない; 'There's no way I'd know'. Casual.
How should I know what he's thinking?
Polite form of 知るわけない. Can be used in formal situations but still conveys 'there's no way I would know'.
How should I know about that matter?
Very strong and dismissive; 'What do I care?' or 'It's none of my business'. Used when the speaker is annoyed at being asked.
How should I know about your schedule? / Like I care about your convenience.
Imply that the question is unreasonable or that the speaker is not the right person to ask.
Direct translations like どうやって知るべきか (dou yatte shiru beki ka) are unnatural and not used. Japanese uses set phrases to convey the rhetorical meaning.
how should I know (literal, unnatural)
知らない (shiranai) is a simple 'I don't know'. 知るか (shiruka) is rough and dismissive. 知るわけない (shiru wake nai) emphasizes impossibility. Choose based on the level of irritation and formality.
A: Where did I put my keys? B: How should I know?
A: What time does the meeting start? B: How should I know? I wasn't invited.
How should I know? Please check with the person in charge.
A: Do you think it will rain tomorrow? B: How should I know? Check the weather forecast.