💡 Detailed Explanation
'～かねない' expresses the possibility of a negative outcome ('could,' 'might'). It's used to show the speaker's personal prediction or worry. Based on the reason 'knowing how careless he is,' the speaker is predicting the negative possibility of 'making a big mistake,' making 'かねない' the right choice. 'に違いない' and 'に相違ない' express strong certainty ('must be'), while 'おそれがある' is more objective and often used in formal warnings (e.g., news reports), making 'かねない' more natural for a personal prediction like this.