King Charles III, 75, and Kate, Princess of Wales, 42, have reportedly “gotten closer” in the wake of their equally shocking cancer diagnoses this year. “The King has always had a close, warm, and unique relationship with the princess,” a palace source recently spilled. “She has a great love and respect for him and his position. When they were in hospital together there was a lot of toddling down the corridor to spend time with her. He has been encouraging and supporting her throughout.” “He’s not a father figure as such — she’s got her own dad to whom she’s absolutely devoted — but you could …