Impossible to comprehend or grasp fully: inconceivable folly; an inconceivable disaster.
So unlikely or surprising as to have been thought impossible; unbelievable: an inconceivable victory against all odds.
American Heritage(R) Dictionary of the English Language, Fifth Edition. Copyright (c) 2011 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.