“Nearly there!” Harry panted as they reached the corridor beneath
the tallest tower. Then a sudden movement ahead of them made them almost drop the crate. Forgetting that they were already invisible, they shrank into the shadows, staring at the dark outlines of two people grappling with each other ten feet away. A lamp flared. Professor McGonagall, in a tartan bathrobe and a hair net, had Malfoy by the ear.
“Detention!” she shouted. “And twenty points from Slytherin! Wandering around in the middle of the night, how dare you ––”
“You don’t understand, Professor. Harry Potter’s coming –– he’s got a dragon!” “What utter rubbish! How dare you tell such lies! Come on –– I shall see Professor Snape about you, Malfoy!”
(Harry Potter and the Sorcerer’s Stone)
Shall is used for saying what you intend to do in the future, and will is used for saying that you are willing to do something or that you intend to do it. Then which is the stronger expression, “I shall see Professor Snape about you” or “I will see Professor Snape about you”?
These remarks are not intended to compete with kiamlaluno’s admirable observations on contemporary use of shall and will, which specifically address OP’s question and which I have upvoted. They are rather addressed to an additional aspect of JKR’s use in the passage at hand.
The use of shall here is more a matter of characterization than semantics.
Hogwarts is a very old-fashioned scene: basically the world of the English Public School as depicted in school stories of the 19th and early-to-mid-20th centuries. A linguistic feature of these tales (I cannot say whether it reflected the reality) has always been that the faculty speak with marked formality, especially to students—the notion being, I suppose, that the faculty are concerned both to provide sound linguistic models and to maintain their own formal authority.
Prof. McGonagall is not only very senior faculty, she is an elderly woman: according to the Harry Potter wiki, she was born in 1935. She thus belonged to a generation which was trained in (as I still was in the 1950s), and which adhered strictly to (as I do not), the “traditional rule” described in kiamlaluno’s NOAD citation: “… shall is used with first person pronouns (I and we) to form the future tense …”
So Minerva McGonagall’s use of shall does not express any heightened determination; it expresses her age, education, and status.
Source : Link , Question Author : Listenever , Answer Author : StoneyB on hiatus