Week 5 - Matching Models: Probabilistic and Language Model - Reading Note

I read:
Christopher D. Manning, Prabhakar Raghavan, Hinrich Schutze, “Introduction to Information Retrieval”. Cambridge University Press. 2008. Chapters 11 & 12.

Djoerd Hiemstra and Arjen de Vries. (2000) Relating the New Language Models of Information Retrieval to the Traditional Retrieval Models. Technical Report, TR-CTIT-00-09, Centre for Telematics and Information Technology

From IIR Chapter 11 & 12, what did I just read? Maybe my brain is not working today but I only was able to form the highest level of understanding. Maybe the chapters were too dense with equations. I'm hoping that the article will make more sense.

From Hiemstra and de Vries (2000), "[Vector space] is based on the similarity between query and document, the [probabilistic model] is based on the probability of relevance, using the distribution of terms over relevant and non-relevant documents."