With regards to a mortal king who is difficult to approach, it is impossible for everyone to merit having their cases heard personally. Instead, all are expected to be judged according to the system of judgment that has been established. However, all who turn to G-d, the King of kings, in heartfelt prayer, will always be heard.
In fact, each person receives a private audience with G-d during his prayers. Accordingly, the words of the Shemoneh Esrei prayer are spoken in a whisper, indicating the close, personal connection that one experiences during his prayers, presenting his requests directly to G-d. We also find that on Rosh Hashana, all of Creation, namely Mankind, passes before G-d to be individually judged in a single moment. So too, G-d receives each of our prayers as if we were the only one praying.
A Related Story:
Jacob, a fifth grade rebbi, wanted to instill in the heart of his eight year old son David the great importance of praying together with the congregation, the tzibur, as well as the immeasurable value of his own personal prayers to G-d. He decided to take him to shul (synagogue) for the first time for the Friday night prayers. He taught his son how to sing the famous Lecha Dodi hymn that is part of “Kabbalat Shabbat”. The custom in their shul was for everyone to read each of the stanzas together as a group. He told his son that G-d would be listening only to him as he sang this special song out loud.
When it came time for David to sing Lecha Dodi he nervously took hold of his Siddur. As he began to sing out loud he was surprised to see everyone else singing with him. Jacob quickly whispered to him not to stop, reminding him that G-d was listening only to him. David continued as his father instructed.
Later, during the Shabbat meal, David explained to his younger brother Moshe Chaim that he wanted to teach him that G-d listens to each person who comes to pray in shul as if he is the only one. He continued to say, “Whenever you go to shul to pray for the rest of your life, whether as the prayer leader or as one of the congregants, you must feel as though you are alone with G-d. If you do this, your prayers will always be precious to G-d.”