Don't tell me you are not getting the picture! From the picture itself current search market condition is quiet evident. If not let briefly discuss it.

From latest buzz from StatCounter Google hold nearly 90% of total search market worldwide. In US search market also Google dominate with 80% market share. So the supremacy of Google is quite inevitable.

On the other hand , after Bing had entered the search market, Yahoo has loss its market share dramatically.

From 17% search market share its share has dropped to 4% only. In US also, Yahoo does not lie in comfort zone. Yahoo have nearly 9% of total search market share of US search. Most worst part of it is that they are continuously loosing their search share globally as well in US.

When Bing launched everyone in the market anticipated that something is going to happen! Believe me or not that "Something" has really took place, which is Google strengthening its position! Promise that Bing made has not kept till date. But surely it made Google to brought some changes, which are actually benefiting surfers worldwide. From stat point of view Bing currently holds 3.5% search market share worldwide and 8.5% of total US search. But good (for improvement of search) thing is that Bing's share is increasing, though very slowly.

Other than these three (In near future it is likely to be Google Vs Bing) Ask has some significant but very low search market share (1%). Ask's share is not varying with the time and it is very unlikely that it can emerge as main contestant in search market. Oh yes I am not forgetting Baidu, the china major. But it's penetration is limited only in china and there is little chance that Baidu can make footprint in Global search market.