Bă (把) construction is used to signal a change of state resulting from certain activity. It is also implied that the activity causing the change of state has already ended.
The sentence *他把書在看t (¯a b˘a sh¯u z`ai k`an) is ungrammatical because such a resulting state is unavailable with a progressive marker z`ai (在) which focuses on the ongoing state of an activity rather than reaching the endpoint of an event.
On the contrary, The end of the sentence 他把書看了 (t¯a b˘a sh¯u k`an le/ He read the book.) is explicitly signaled by the perfect-aspect marker -le (了), thus indicating a new state resulting from the implementation of the event.
Reference: Chinese: a linguistic introduction by Chao Fen Sun