Kamsa agreed to the logical arguments of Vasudeva, and, having full faith in Vasudeva's words, he refrained from killing his sister. Vasudeva, being pleased with Kamsa, pacified him further and entered his own house - SB 10.1.55

Expressions researched:
"Kaṁsa agreed to the logical arguments of Vasudeva, and, having full faith in Vasudeva's words, he refrained from killing his sister. Vasudeva, being pleased with Kaṁsa, pacified him further and entered his own house"

Srimad-Bhagavatam

SB Canto 10.1 to 10.13

Śrīla Śukadeva Gosvāmī continued: Kaṁsa agreed to the logical arguments of Vasudeva, and, having full faith in Vasudeva's words, he refrained from killing his sister. Vasudeva, being pleased with Kaṁsa, pacified him further and entered his own house.

SB 10.1.55, Translation and Purport

Śrīla Śukadeva Gosvāmī continued: Kaṁsa agreed to the logical arguments of Vasudeva, and, having full faith in Vasudeva's words, he refrained from killing his sister. Vasudeva, being pleased with Kaṁsa, pacified him further and entered his own house

Although Kaṁsa was a sinful demon, he believed that Vasudeva would never deviate from his word. The character of a pure devotee like Vasudeva is such that even so great a demon as Kaṁsa firmly believed in his words and was satisfied. Yasyāsti bhaktir bhagavaty akiñcanā sarvair guṇais tatra samāsate surāḥ (SB 5.18.12). All good attributes are present in a devotee, so much so that even Kaṁsa believed in Vasudeva's words without a doubt.