to hope very strongly that something will happen even though you know it is not likely

यह उम्मीद करना कि कुछ होगा, भले ही आप जानते हों कि यह संभव नहीं है

English Usage: She waited, hoping against hope, that he would return.

Hindi Usage: वह प्रतीक्षा करती रही, निराशा में उम्मीद करते हुए, कि वह लौट आएगा।