No (doubt/hope), There is no way, It is impossible, Not a hope in hell
Structure
Verb + べくもない
するVerb + す(る) + べくもない
(A) べくもない is a formal written expression used when there is no possibility of (A) happening at all. It generally follows expressions like 望む、疑う、知る、比べる、及ぶ、考える、否定、かなう、勝つ、想像する, and does not appear in daily conversation.