In The Odyssey, Book 19, what is the immediate context of this conversation between Odysseus and Penelope?
In Book 18, the suitors have just engineered a conflict for their own amusement between the disguised Odysseus and Iros, an angry beggar who mistreats Odysseus and insults him. The shame that this brings on Penelope's household is not lost on her. However, the suitors go off, leaving the hall. Odysseus and his son Telemachus then remove all weapons and armour from the hall, stowing them safely upstairs as part of their plan. Telemachus leaves his father in the hall, where he is soon joined by Penelope, wanting to know more about this stranger in her midst.
Of course, Odysseus weaves her a story completely in keeping with his character, saying that he was a prince who had entertained Odysseus for twelve days. When Penelope asks for more details, he manages to convince her of the truth of what he is saying. However, she does not have much hope for any possibility of being reunited with her husband. She appears to feel her situation is hopeless.