I remember one of our teachers in our school life, he instructed that, "If you always think that, 'I shall pass my examination with distinction,' then you can pass in first division. If you think that 'I shall pass my examination in the first division,' then you may pass in the third division. And if you think that, 'I shall some way pass my examination in the third division,' then you will fail." That means if you expect more than your capacity, then it may be possible that at the time of examination you get the right number and pass your exam.
So the chanting of Hare Kṛṣṇa mantra, Caitanya Mahāprabhu has said, sadā, kīrtanīyaḥ sadā hariḥ: not that two hours or one hour, but one should practice. And that is the recommendation as it was followed by Haridāsa Ṭhākura. But because we cannot do that, therefore we have to engage always in the service of Kṛṣṇa. That will make me remembering Kṛṣṇa. The real fact is how to remember Kṛṣṇa.
So this remembering of Kṛṣṇa by Ajāmila was not accidental. He chanted. He served Nārāyaṇa in his previous life when he was young man, but by bad association he fell down. But the effect was there at the time of his death, so much effective that the Viṣṇudūta recommends that "Because he has chanted at the time of his death the holy name of Lord, he is now free from all sinful reaction."