Answer
A devotee's life is completely under the control of Prārabdha karma and Kṛṣṇa, but how Kṛṣṇa chooses to deal with a devotee's karma is entirely His decision.
It is not correct to say that a devotee's devotional service has no relationship with prārabdha karma. The devotee's activities, devotional service, and spiritual progress may all have some bearing on how prārabdha karma manifests, if the Lord so desires. Karma itself is also the Lord's arrangement, operating through the law of karma.
If, through the law of karma, a particular result is meant to remain, the Lord may retain it and engage the devotee in devotional service through that very circumstance. Therefore, karma and devotional service are not completely unrelated. However, karma is no longer binding upon a devotee in the ordinary sense.
A conditioned soul cannot move even an inch beyond the limits of his karma. He cannot obtain one rupee more than what is allotted by his prārabdha karma. But in the case of a devotee, the situation is different. The same karma that was supposed to yield one rupee may, by Kṛṣṇa's arrangement, yield one hundred rupees if that is required for the Lord's service. Kṛṣṇa supplements what is needed.
That is the meaning behind the statement that devotional service can change our karma.
If all prārabdha karma were completely removed, we could not continue to remain in this material body, because the body itself is a result of prārabdha karma. From the moment of birth, as time unfolds, different karmic seeds mature and bear fruit. In one year certain results appear, in another year different results appear. These karmic reactions are already present in seed form.
However, when we become devotees of the Lord, prārabdha karma continues to exist, but it is no longer independently binding. Kṛṣṇa may decide to remove certain karmic reactions altogether.
He may think, "This particular reaction does not help My devotee's spiritual progress. It unnecessarily disturbs his devotional service." In such cases, He may reduce or eliminate it. But this decision is made according to the Lord's estimation, the Paramātmā's estimation, and the guru's estimation—not according to our estimation.
Sometimes we become sick and wonder, "Why is Kṛṣṇa not removing this illness? It is preventing me from performing devotional service." But perhaps the devotional service Kṛṣṇa wants from us at that moment is to learn detachment from the body, to understand the laws of karma more deeply, or to develop humility and dependence on Him.
If the Lord desires that someone remain bedridden for a period of time, then that itself becomes part of the devotee's spiritual journey. Perhaps the original karmic reaction was meant to be much more severe, but Kṛṣṇa has already reduced it. Whatever we experience is ultimately sanctioned by the Lord.
Therefore, a devotee sees no accident in life. Nothing happens independently of the Lord's will. Material nature may be carrying out its laws, but those laws operate only with the Lord's sanction.
A devotee thinks, "Kṛṣṇa could have stopped this if He wished. Since He has not stopped it, there must be some purpose behind it."
Consider devotees collecting donations. All wealth belongs to Kṛṣṇa, and Kṛṣṇa knows exactly who is willing to contribute and who is not. If He wished, He could send the devotee only to receptive people. Yet sometimes He sends a devotee to someone who refuses, insults him, or humiliates him.
Why?
Because Kṛṣṇa may be teaching that devotee detachment, humility, tolerance, or dependence upon Him. Every situation becomes an opportunity for spiritual growth.
Therefore, the interaction between a devotee and karma is dynamic. One should not make simplistic statements such as, "A devotee's life has nothing to do with karma."
Why do people look different? Why do they possess different abilities and capacities? Karma certainly plays a role. Yet for a devotee, karma is continually modified by Kṛṣṇa's reciprocation.
If your sincere desire is to serve the Lord, Kṛṣṇa may supplement whatever is lacking. This is the meaning of His promise: "I preserve what My devotee has, and I carry what he lacks."
Suppose you require some facility to perform Kṛṣṇa's service. By ordinary karmic calculation you may not possess it, but Kṛṣṇa can provide it.
This introduces another principle in addition to the law of karma—the law of surrender.
Ordinary people live under the law of karma. Devotees learn to live under the law of surrender. They constantly seek Kṛṣṇa's reciprocation through sincere surrender.
Kṛṣṇa consciousness is fundamentally a process of transformation at the level of consciousness.
A devotee does not think like a karmī. A king may appear to control an entire kingdom, but a true king understands that he is only acting as a representative of the Supreme Lord. Whether one possesses great power or very little power makes no essential difference. The real proprietor remains the same—the Supreme Lord.
When this understanding develops, one's relationship with karma changes. One no longer sees life merely as a sequence of karmic reactions but as a personal arrangement made by Kṛṣṇa for one's spiritual advancement.