~ 아닌 가 싶다 = It is probably ~ / I suspect ~ (Ex) It is probably ther were right. (그들이 옳았던 게 아닌가 싶다.) I suspect there was some monkey business between them. (그들간에 부정한 일이 있었던게 아닌가 싶다.)

~아닌가 싶다 is used when you express your opinion with uncertainty. ~아닌가 싶다 = I think that S + V but I'm not sure. 나는 그가 범인이 아닌가 싶다 -> I think that he is the criminal but I'm not sure.